Variance change point detection method and system and computer readable storage medium

Abstract

The present disclosure provides a variance change point detection method and system and a computer-readable storage medium. The present disclosure provides a method for detecting variance change points of a target time series based on a baseline assumption of statistical stationarity. The target time series signal is modeled as including a trend component signal and a residual component signal. For the target signal, a signal cost function including at least a difference penalty function and at least one regularization term is optimized to output the trend component signal of the target signal. For the residual component signal, a signal cost function including at least a difference penalty function and at least one regularization term is optimized to output the estimated variance of the residual component signal. The two cost functions can be optimized by applying an augmented Lagrangian operator. A centralized cumulative sum is calculated based on the cumulative sum of the estimated variances. The centralized cumulative sum is segmented to generate variance change points of the centralized cumulative sum. Compared with existing methods, such a method can provide improved performance.

Description

Technical Field

[0001] The present disclosure relates to a variance change point detection method and system, and a computer-readable storage medium. Background Art

[0002] Change point detection is an aspect of statistical analysis of time series data. Time series data relating to events, phenomena, measurements, etc. may be observed over time. The values ​​of variables observed from the time series data may vary over time; however, such variations may indicate a trend change over time, or may simply indicate an outlier. Various probability distributions known to those skilled in the art describe how the values ​​of a variable in the time series data are expected to be distributed over time. By observing changes in these probability distributions, change points in the time series data may be more easily identified.

[0003] In methods of change point detection, measures of statistical confidence (such as standard deviation) may also be calculated and observed over time. Variance change point detection is a change point detection method in which the variance calculated based on the standard deviation is observed over time. Such methods attempt to observe changes in the variance (a measure of statistical confidence) over time as an indication that a trend change point has been observed to occur over time. Given a trend in time series data with random values ​​that are expected to fall along a particular probability distribution (this distribution is often referred to as a "prior"), the variance of the variable over time can be calculated based on the standard deviation based on the probability distribution using established statistical analysis methods. For example, the prior may be a Gaussian distribution (a "Gaussian prior").

[0004] Time series data and their trends are increasingly observed in contexts that generate large amounts of data, such as distributed computing, cloud computing, machine learning, data centers, financial systems, e-commerce transactions, etc. In addition, time series data and their trends may be time-sensitive, which means that statistical analysis of time-sensitive trends may need to be fast enough to quickly generate actions or actionable outputs. Therefore, there is a need to provide improved change point detection so that when a change point occurs in time, the change point can be detected quickly, so that rapid actions and responses can be taken to the change point. Summary of the invention

[0005] The present disclosure provides a variance change point detection method, which includes the following steps: optimizing a variance filtering signal cost function for a residual component signal of a target signal of a time series to output an estimated variance of the residual component signal; calculating a time-centered cumulative sum of the estimated variance of the residual component signal; and segmenting the centered cumulative sum to generate one or more variance change points of the target signal.

[0006] The present disclosure also provides a variance change point detection system, which includes: one or more processors; and a memory, which is communicatively connected to the one or more processors, and the memory stores computer executable modules that can be executed by the one or more processors. When executed by the one or more processors, the computer executable modules perform associated operations, and the computer executable modules include: a variance filtering module, which further includes a variance filtering cost function optimization module, which is configured to optimize the variance filtering signal cost function for the residual component signal of the target signal of the time series to output the estimated variance of the residual component signal; and a change point positioning module, which further includes: a centralized cumulative sum calculation submodule, which is configured to calculate the centralized cumulative sum of the estimated variance of the residual component signal in time; and a segmentation submodule, which is configured to segment the centralized cumulative sum to generate one or more variance change points of the target signal.

[0007] The present disclosure also provides a computer-readable storage medium, which stores computer-readable instructions that can be executed by one or more processors. When executed by the one or more processors, the computer-readable instructions cause the one or more processors to perform operations, including: optimizing a variance filtering signal cost function for a residual component signal of a target signal of a time series to output an estimated variance of the residual component signal; calculating a time-centered cumulative sum of the estimated variance of the residual component signal; and segmenting the centralized cumulative sum to generate one or more variance change points of the target signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The detailed description is set forth with reference to the accompanying drawings. In the drawings, the left-most digit(s) of a reference number identifies the drawing in which the reference number first appears. The use of the same reference numbers in different drawings indicates similar or identical items or features.

[0009] Figure 1 A flowchart of a variance change point detection method according to an example embodiment of the present disclosure is illustrated.

[0010] Figure 2 A flow chart of a trend component removal sub-method according to an example embodiment of the present disclosure is illustrated.

[0011] Figure 3 A flow chart of a variance filter method according to an example embodiment of the present disclosure is illustrated.

[0012] Figure 4A flow chart of a change point locator method according to an example embodiment of the present disclosure is illustrated.

[0013] Figure 5A and Figure 5B A system architecture of a system configured to compute variance change point detection according to an example implementation of the present disclosure is illustrated.

[0014] Figure 6 An architectural diagram of a server host and a computing host for computing resources and a time series trend model according to an example implementation of the present disclosure is illustrated.

[0015] Figure 7 An example computing system for implementing the processes and methods described herein for implementing variance change point detection is illustrated.

[0016] FIG. 8A to FIG. 8D Examples of synthetic time series datasets generated with randomly generated noise, multiple randomly generated anomalies, and trends exhibiting non-stationarity are illustrated. DETAILED DESCRIPTION

[0017] The systems and methods discussed herein relate to implementing a time series trend model, and more specifically, to implementing data cleaning and data sparsity regularization for a time series model, and a variance change point detection algorithm for a time series model.

[0018] According to an example embodiment of the present disclosure, a time series trend model may include a set of equations adapted to the observation of variable values, such as, for example, a regression model. The equations of the time series trend model may be calculated based on the trend of the observed data in the target time series over time, with time as the independent variable (the value of the target time series over time is then referred to as the "target signal"). Modeling the target signal as a set of equations may assume that the target signal may be modeled as the sum of at least two component time series (a trend component time series and a residual component time series). Each of the trend component time series and the residual component time series may be a time series of the same length as the target time series. Each of the trend component time series and the residual component time series may be further modeled as one or more equations, respectively.

[0019] For example, the regression model can be a linear model in which the variable is modeled as a linear function of time based on the expectation that the variable value will fall along a Gaussian distribution ("Gaussian prior"). Alternatively, the regression model can be, for example, a nonlinear model (such as a logarithmic model, an exponential model, etc., but not limited to this). The regression model can be selected based on the prior of the variable of the target time series, which should not be limited to a Gaussian prior and can include, for example, a binomial distribution, a Bernoulli distribution, a Laplacian distribution, etc., and therefore, the regression model can be, for example, a generalized linear model based on a given prior.

[0020] For example, according to an example embodiment of the present disclosure, the target signal y may include values ​​observed over a series of N time periods {0, 1, ..., N-1}, where any time period of substantially equal duration may generally be referred to herein as a "period". Thus, these values ​​may be written as y = [y0, y1, ..., y N-1 ] T Therefore, the target signal y can be modeled as a function of time t, where t is an arbitrary period of time.

[0021] According to an example embodiment of the present disclosure, the target signal y can be modeled as a function of additional component time series, each of which is modeled as a function of time t. The modeling function can be, for example, a sum or weighted sum function over the component time series. Like the target signal, the component time series can include values ​​observed over a series of N time periods.

[0022] The component time series may include a trend component time series and a residual component time series. These two component time series represent the following assumption: after subtracting those components of the target signal attributable to the trend in the target signal in time from the value of the target signal in time (the components themselves can be modeled as a function of time (these subtracted components in time are subsequently referred to as "trend component signals")), a residual component will be generated, which reflects the influence of noise and outliers in time (these residual components in time are subsequently referred to as "residual component signals").

[0023] For example, according to an exemplary embodiment of the present disclosure, the trend component signal τ can be written as τ=[τ0, τ1, ..., τ N-1 ] T , and the trend component signal τ can be modeled as a function of time t. The residual component signal r can be written as r = [r0, r1, ..., r N-1 ] T , and the residual component signal r can be modeled as a function of time t.

[0024] Therefore, in general, y = τ + r, and for time t, yt =τ t +r t .

[0025] Each r of the residual component signal t can be further divided into noise subcomponent n t and the abnormal subcomponent a t These subcomponents represent the probability that one or both of the noise and the anomaly will not contribute to the observation of the target signal y at time t. Therefore, the individual r of the residual component signal t It can be written as r t =n t +a t , where for any given time t, n t and a t Either, both, or neither of has a zero value (when modeled as not contributing to the target signal y at time t) or a non-zero value (when modeled as contributing to the target signal y at time t).

[0026] According to an example embodiment of the present disclosure, it is assumed that M change points can be identified in the residual component signal r in time, wherein the M change points represent points along the residual component signal r at which the variance σ of the residual component signal r is 2 (i.e., the square of the standard deviation) changes significantly (the definition of such significant changes and the method for detecting such significant changes will be given in the subsequent paragraphs of this article). Based on the assumption of M change points, the target signal y can be modeled by a piecewise regression model, wherein the overall target time series can be segmented into M+1 time series segments separated by M change points. Each time series segment in the time series segmentation can be modeled as the time series trend model described above. Based on this assumption, the M+1 separated time series trend models can be approximated together as a model of the entire target time series.

[0027] Typically, starting from a target signal y, it is expected to remove a trend component signal τ to produce a residual component signal r, and it is expected to remove the residual component signal r to produce a trend component signal τ. Trend removal and residual removal can serve different purposes in terms of statistical analysis. According to an example embodiment of the present disclosure, removal of the trend component signal τ can convert the target signal y into a piecewise statistically stationary time series signal. Statistical stationarity can refer to a time series signal having a statistical distribution that does not vary in time so that a measure of statistical confidence (such as variance σ 2 ) also does not vary in time. Therefore, based on such a time series signal, variance change point detection can be facilitated based on the fact that variance changes should no longer be attributed to trends in time.

[0028] Since the trend component signal τ describes a function that varies in time, the trend component signal τ can have a statistical distribution and can have a measure of its statistical confidence that varies in time. Therefore, it can be expected that removing the trend component signal τ from the target signal y will remove the main contribution to the statistical distribution and the measure of the statistical confidence that varies in time of the target signal y. Therefore, it is expected that the remaining component of the target signal y is subject to a measure of the statistical confidence that varies in time of the target signal y (such as the variance σ) compared to the original target signal y. 2 ), although whether the residual component of the target signal y is completely statistically stationary cannot be guaranteed and may depend on the details of each modeled time series on a case-by-case basis. For the purposes of the example embodiments of the present disclosure, it should be understood that the residual component of the target signal y can be considered to be approximately and substantially statistically stationary.

[0029] In addition, since it is assumed above that the component time series of the target time series includes a trend component time series and a residual component time series, the remaining component of the target signal y can be considered as a residual component signal r.

[0030] According to the exemplary embodiments of the present disclosure, change point detection, especially variance change point detection, is based on the following assumption: the target time series exhibits statistical stability without any change points. Therefore, unless there is a change point, it is expected that the removal of the trend component signal τ will transform the target signal y to meet this premise. On the contrary, after the trend component signal τ is removed, the target time series still does not exhibit statistical stability (i.e., the variance σ 2 Still changing in time), then there are change points in the target time series.

[0031] The exemplary embodiments of the present disclosure provide a variety of methods for executing the above-mentioned variance change point detection method, wherein the variance change point detection method at least includes a trend component removal method, a variance filtering method, and a change point location method.

[0032] Figure 1 The flowchart of the variance change point detection method 100 according to an example embodiment of the present disclosure is illustrated. The variance change point detection method further includes a trend component removal sub-method 200, a variance filtering sub-method 300 and a change point location sub-method 400. Each of these sub-methods will be described in turn below.

[0033] Figure 2 A flow chart of a trend component removal sub-method 200 according to an example embodiment of the present disclosure is illustrated.

[0034] In step 202, a target signal of a target time series is obtained.

[0035] According to an example embodiment of the present disclosure, the target time series may be any time series having a variable whose value changes over time as described above. The target signal may be the value of the variable of the time series observed over time.

[0036] In step 204, a signal cost function is optimized for the target signal to output a trend component signal of the target signal, wherein the signal cost function may include at least a difference penalty function and at least one regularization term.

[0037] The difference penalty function may generally be referred to as a loss function, which is solved to optimize the difference between the two signals. It is known in the art that a loss function may be an arbitrarily defined function based on an input, wherein the function performs one or more operations to return an output. (However, "cost function" and "loss function" may generally be used interchangeably, and for the purpose of clearly understanding the present disclosure only, "signal cost function" should be understood to refer to the function optimized in step 204, and "loss function" should generally be understood to refer to any cost function or loss function.) According to an example embodiment of the present disclosure, the input of the difference penalty function may be the difference between the two signals, specifically the difference of the target signal y minus the trend component signal τ. According to an example embodiment of the present disclosure, the loss function may be defined to impose a greater penalty on a larger difference between the two signals, and a smaller penalty on a smaller difference between the two signals. Note that the loss function may be optimized for the trend component signal without knowing the trend component signal.

[0038] According to an example implementation of the present disclosure, the loss function may be a Huber loss function, which is generally defined as follows:

[0039]

[0040] According to the Huber loss function, for a defined threshold γ (which should be a relatively small value), the output of the Huber loss function is always positive; for inputs between ±γ, the output of the Huber loss function is quadratic, including 0; for inputs greater than +γ, the output of the Huber loss function increases linearly; and for inputs less than –γ, the output of the Huber loss function increases linearly.

[0041] Therefore, in the context of the difference penalty function, a larger difference between the target signal y and the trend component signal τ (according to the time series trend model as described above, the larger difference is the residual component signal r) will incur a larger penalty (regardless of whether the larger difference is positive or negative). Therefore, optimizing for the difference penalty function will tend to minimize the residual component signal r on the target time series as much as possible (and, as a result, maximize the trend component signal τ on the target time series as much as possible).

[0042] According to an example embodiment of the present disclosure, at least one regularization term can be used to reduce the impact of trend changes over time. For example, the regularization term can be a difference regularization term, in which the signal is multiplied by a difference matrix. The regularization term can be a Lasso (l1) regularization term represented by the operator || ||1. The Lasso regularization term typically includes a regularization parameter that is multiplied to control the size of the regularization term, which can be an arbitrarily set hyperparameter λ and is not determined by the steps of the method described herein. The hyperparameter λ can be set based on the expected strength of the regularization effect described herein according to experimental results.

[0043] According to example embodiments of the present disclosure, the Lasso regularization term typically outputs a sparse signal in which most coefficients are zero, reflecting a model that follows a Laplace prior; based on the Laplace distribution, the Lasso regularization term tends to push small values ​​of the signal to zero. The reasons for the sparse output by the Lasso regularization term are generally known to those skilled in the art, and do not need to be reiterated herein to understand the present disclosure. However, due to the sparse nature of the Lasso regularization output, the regularization effect of each regularization term in the regularization term on the difference penalty is also sparse. According to the following results given in the subsequent Table 1, it has been observed that better results are achieved compared to non-sparse regularization terms.

[0044] Furthermore, at least one of the regularization terms may be a difference regularization term, wherein the signal is multiplied by a difference matrix, wherein the off-diagonal coefficients of the matrix tend to be mostly zero values, as described in more detail below.

[0045] The difference matrix usually refers to a band matrix with a main diagonal and at least one subdiagonal or superdiagonal or a combination thereof, and all other coefficients are zero. It depends on whether the difference matrix is ​​a first-order difference matrix D (1) , the second-order difference matrix D (2) Or a high-order difference matrix D (k) , the band and its value can be different. The first-order difference matrix D is given below (1) and the second-order difference matrix D (2) Example:

[0046]

[0047] Intuitively, we can apply k-order (k=1, 2, ...) differences to measure the k-th difference of the time series. For example, we can use the first-order difference matrix with the vector format [y1, y2, ..., y N ] can result in the conversion of each coefficient of the signal into the difference between the previous coefficient: [y2-y1, ..., yN- y N-1 ], which takes into account the differences between consecutive entries in the input time series. The second-order difference matrix is ​​combined with the vector of the form [y1, y2, ..., y N ] time series multiplication can result in the signal being converted into the difference between each coefficient of the signal and the first two coefficients: [y 2- 2y1+y3,...,y N-2 y N-1 +y N-2 ], which takes into account the difference between first-order differences or second-order differences. Both can further reduce the contribution of the trend component signal τ to the target signal y in time. Therefore, the first-order difference regularization term can incorporate the first-order difference matrix, the second-order difference regularization term can incorporate the second-order difference matrix, and so on (as well as two arbitrarily set regularization hyperparameters λ).

[0048] According to an example implementation of the present disclosure, the following signal cost function adds both a first-order difference l1 regularization term (incorporated with a first-order difference matrix) and a second-order difference l1 regularization term (incorporated with a second-order difference matrix) to a difference penalty function (in this article, the difference penalty function is a Huber loss function):

[0049] g γ (y-τ)+λ1||D (1) τ||1+λ2||D (2) τ||1.

[0050] The optimization of the above signal cost function can be written as follows:

[0051]

[0052] According to example embodiments of the present disclosure, without limiting the loss function and without limiting one or more regularization parameters, optimizing a cost function such as the above example signal cost function can generally describe the regularization filtering performed on the target signal and the trend signal. Specifically, the loss function of the regularization filtering can be performed on the difference between the target signal y and the trend signal τ. According to the time series trend model described above, it is expected that this will generate a trend component signal (written as t in this article to distinguish) separately. ).

[0053] At step 206, a residual component signal is obtained by subtracting the difference of the trend component signal from the target signal.

[0054] This step can thus be written simply as:

[0055]

[0056] Figure 3A flow chart of a variance filter method 300 according to an example implementation of the present disclosure is illustrated.

[0057] In step 302, the residual component signal of the target signal is squared.

[0058] Because the variance is, by definition, the square of the standard deviation of the time series, the residual component signal can be normalized to model a linear relationship with its variance by squaring the residual component signal. The residual component signal represented as a vector can be squared by squaring each of its coefficients. Therefore, the squared residual component signal, denoted as s in this article, can be derived as follows:

[0059]

[0060] In step 304, a signal cost function is optimized for the squared residual component signal to output an estimated variance of the squared residual component signal, wherein the signal cost function may include at least a difference penalty function and at least one regularization term.

[0061] According to the basic principles given above, in the absence of any change points, it is expected that the residual component signal and its square in time will show statistical stationarity. However, according to the example embodiments of the present disclosure, without actual measurement of the statistical confidence of the residual component signal, the variance of the residual component signal cannot be directly measured and should be estimated. Specifically, the square s of the residual component signal can be modeled as a linear relationship with the variance v of the residual component signal.

[0062] Those skilled in the art will appreciate that variance estimation for a regression model (where the coefficients of the model are unknown, such as in the context of variance change points discussed herein) is generally an open problem in the art, and various computational methods are known. For example, one type of variance estimation method, or simply "estimator," is a Lasso estimator, which may also include a hyperparameter λ3, as described above with reference to the Lasso regularization term. Due to the expected sparsity of the residual component signal, the Lasso estimator may be applied to the variance estimation of the residual component signal; due to the Lasso regularization term of the trend component removal submethod 200 as described above, the residual component signal is expected to be sparse, so the Lasso estimator may also be applied thereto for similar reasons as described above.

[0063] The known Lasso estimator applied to the linear relationship between the square s of the residual component signal and the variance v of the residual component signal may, for example, have the following general form:

[0064]

[0065] In this article, the operator is the l2 loss term, and the operator ||||1 is the l1 regularization term. However, it is generally understood that the l2 loss follows a Gaussian prior. Therefore, the l2 loss will not be robust to anomalies within the residual component signal. Therefore, according to an example embodiment of the present disclosure, the l2 loss term of the general Lasso estimator can be replaced by another term.

[0066] According to an example embodiment of the present disclosure, the l2 loss term of the general Lasso estimator can be replaced by the Huber loss function. As described above, since the Huber loss function is linear for large inputs, rather than quadratic like the l2 loss, the Huber loss function tends to mitigate the loss caused by large inputs, thereby supplementing the Laplace prior instead of the Gaussian prior. According to the following results given in the subsequent Table 1, it has been observed that better results are obtained compared to the l2 loss term.

[0067] The performance of various methods is measured based on relaxed precision, recall, and F1 score (where, in each case, the closer the score is to 1, the better the performance).

[0068]

[0069] It can be seen that in the presence of the l2 regularization term and the absence of the Huber loss function, the performance degrades. Therefore, the Lasso estimator according to the example implementation of the present disclosure can be updated to the following form:

[0070] g γ (sv)+λ3||D (1) v||1

[0071] The optimization of the above signal cost function can be written as:

[0072]

[0073] According to example embodiments of the present disclosure, optimizing a signal cost function such as the example signal cost function described above can generally describe a variance estimator that estimates the variance of a squared residual component signal over time. Specifically, a loss function that performs regularized filtering on the square of the residual component signal s minus the variance v of the residual component signal can be used. Based on the linear equations modeled between them as described above, it is expected that this will produce a variance estimate (written herein as ) as a time series for the sake of distinction. and is defined as follows).

[0074]

[0075] Example embodiments of the present disclosure also provide an augmented Lagrangian function that operates to optimize either or both of the above-mentioned signal cost functions.

[0076] As known to those skilled in the art, the above-mentioned signal cost function can be optimized by the operation of a known optimization algorithm such as gradient descent or proximal gradient. However, according to an example embodiment of the present disclosure, due to the multiple constraints of the signal cost function therein, instead of optimizing the signal cost function, an augmented Lagrangian method can be optimized instead, wherein each of the constraints is rewritten as a penalty term of the signal cost function, resulting in an augmented Lagrangian function. In addition, the augmented Lagrangian function can be solved by an alternating direction method of multipliers ("ADMM") method, wherein, in alternating iterations, the augmented Lagrangian function is solved in order to minimize one parameter while maintaining another parameter. The ADMM method can also be a method based on optimization-minorization ("MM-ADMM").

[0077] First, the above signal cost functions can be rewritten in the following form:

[0078]

[0079] stDτ=z.

[0080] By setting a = y, b = τ and D = [λ1D (1)T ,λ2D (2)T ] T To make the above formula equivalent to the signal cost function of the trend component removal sub-method 200. By setting a=s, b=v and D=λ3D (1) to make the above formula equivalent to the signal cost function of the variance filter method 300.

[0081] According to an example embodiment of the present disclosure, the augmented Lagrangian function may have the form written as follows Using additional dual variables The augmented Lagrangian function can alternately solve for b while keeping each other parameter constant (and then update each variable), and solve for z while keeping each other parameter constant (and then update each variable):

[0082]

[0083] According to the MM-ADMM method, the augmented Lagrangian function can be optimized by the following iterative steps similarly applied to both of the above signal cost functions:

[0084] b k+1 =y-ρ(A+ρD T D) -1 D T (u k -z k +Dy)

[0085] z k+1 =S ρ (Db k+1 +u k )

[0086] u k+1 =u k +Db k+1 -z k+1 .

[0087] That is, first, while keeping u k and z k While keeping constant, solve b k+l ; Then, while maintaining b k+1 and u k While keeping z constant k+1 ; Then, while maintaining b k+1 and z k+1 While keeping u constant k+1 .

[0088] The iteration step also includes a matrix A. According to an example implementation of the present disclosure, A can be solved as follows:

[0089] A=diag(g γ ′(a k -b k ))diag -1 (g γ ′(a k -b k )).

[0090] The iteration step also includes a soft threshold operator S ρ (x). According to an exemplary embodiment of the present disclosure, S ρ (x) can be solved as follows:

[0091] S ρ (x) = (1-ρ / |x|) + x.

[0092] Figure 4 A flow chart of a change point locator method 400 according to an example implementation of the present disclosure is illustrated.

[0093] In step 402, a temporally centered cumulative sum of the estimated variance of the residual component signal is calculated.

[0094] In the context of example embodiments of the present disclosure, a cumulative sum ("CUSUM") generally refers to summing the values ​​of the time series up to each time k over a series of N time periods {0, 1, ..., N-1}. Each of these sums constitutes a new time series, C = {C0, C1, ..., C N-1},in, Expected C k C always increases in time and at each statistically significant deviation from the expected statistical stationarity along the target signal y, k More significantly increased.

[0095] Conventionally, a CUSUM can be used for change point detection by detecting when the value of the CUSUM time series exceeds a threshold. However, because variance change point detection is based on statistically significant changes rather than an absolute threshold, this approach is not suitable for CUSUMs according to example embodiments of the present disclosure. Furthermore, it is expected that multiple variance change points will be detected, which further makes the use of an absolute threshold inappropriate.

[0096] At step 404, a centered cumulative sum is calculated based on the cumulative sum.

[0097] According to an exemplary embodiment of the present disclosure, the CUSUM time series C k It can be further concentrated to produce a concentrated CUSUM time series C′ k "Concentration" is a calculation defined by the following formula according to an example implementation of the present disclosure:

[0098]

[0099] According to an example embodiment of the present disclosure, over time, where the residual component signal exhibits a statistically significant change in variance (contrary to expectations of statistical stationarity), the concentrated CUSUM tends to increase in time because the first term of the concentrated CUSUM increases at a relatively larger rate over time than the second term of the concentrated CUSUM. However, over time, where the residual component signal does not exhibit a statistically significant change in variance (consistent with expectations of statistical stationarity), the concentrated CUSUM tends to decrease in time because the second term of the concentrated CUSUM increases at a relatively larger rate over time than the first term of the concentrated CUSUM.

[0100] Thus, although the CUSUM time series always increases in time, the concentrated CUSUM time series may exhibit oscillations between increasing and decreasing in time in a near piecewise linear segmentation, changing from one trend to another at variance change points. The piecewise linear nature of the piecewise segmentation facilitates the identification of the change points between increasing and decreasing trends as variance change points.

[0101] At step 406, the centered cumulative sum is segmented to generate variance change points of the centered cumulative sum.

[0102] It should be understood that with respect to a time series, there are various methods to detect various events that may occur along the time series in order to demarcate the edges of different segments between them, or to detect various segment-by-segment trends along the segments of the time series and distinguish the various segment-by-segment trends from segment-by-segment trends along other segments. For the purposes of the example embodiments of the present disclosure, a method of segmenting a time series, whether by detecting events that demarcate the edges of different segments or by detecting the segment-by-segment segments themselves, may be referred to as "segmentation."

[0103] For example, according to an exemplary embodiment of the present disclosure, segmentation may be performed by a breakpoint detection method known to those skilled in the art.

[0104] In the context of time series, a breakpoint may refer to a point along the time series where a sudden change occurs. A "change" may be defined as a change in any observable measure of the time series (such as a statistical distribution over time or any other suitable measure known to those skilled in the art); thus, breakpoint detection may include detection methods based on detecting a sudden change in time of any such suitable measure along the time series.

[0105] For example, according to an example embodiment of the present disclosure, segmentation may be performed by a peak and / or valley detection method known to those skilled in the art.

[0106] In the context of time series, peaks and valleys may refer to points along the time series that are local maxima and local minima, respectively. Like breakpoints, peaks and valleys may represent abrupt changes along the time series. Thus, peak and / or valley detection may include detection methods based on detecting local maxima and local minima in time along the time series.

[0107] For example, according to an exemplary embodiment of the present disclosure, segmentation may be performed by a piecewise regression method known to those skilled in the art.

[0108] The piecewise regression method may refer to various regression methods that model a time series as multiple separate piecewise time series separated at various points. For example, the piecewise regression method described above with respect to the breakpoint detection method may detect breakpoints and use the detected breakpoints as the edges of each separately modeled segment. Alternatively, the piecewise regression may model arbitrary segments of the time series and combine these arbitrary segments to validate the segmentation, and then divide the edges between the validated segments as breakpoints. The piecewise regression method may result in segmenting the centralized cumulative sum time series by any of the means known to those skilled in the art or by any other means.

[0109] Finally, regardless of the detection method, the point where the mutation occurs can be generated as a variance change point through the change point locator method 400 described in this article.

[0110] Example embodiments of the present disclosure may be implemented on a server host and a computing host. The server host may be any suitable networked server, such as a cloud computing system, which may provide a collection of servers hosting computing resources, such as a database containing time series data. According to example embodiments of the present disclosure, a computing host such as a data center may host a time series trend model to perform a variance change point detection method.

[0111] The cloud computing system can be connected to various end devices, which users can operate to collect time series data, organize data, set parameters, and run time series trend models to perform variance change point detection. The end device can be connected to the server host through one or more networks (such as edge nodes of the cloud computing system). The edge node can be any server that provides outbound connections from other nodes connected to the cloud computing system, and thus can divide the logical edge of the network of the cloud computing system, without having to be a physical edge. In addition, the edge node can be an edge-based logical node that deploys non-centralized computing resources of the cloud computing system, such as cloudlets, fog nodes, etc.

[0112] Figure 5A and Figure 5B A system architecture of a system 500 configured to compute variance change point detection according to an example implementation of the present disclosure is illustrated.

[0113] The system 500 according to an example embodiment of the present disclosure may include one or more general-purpose processors 502 and one or more special-purpose processors 504. The general-purpose processor 502 and the special-purpose processor 504 may be physical or may be virtual and / or distributed. The general-purpose processor 502 and the special-purpose processor 504 may execute one or more instructions stored on a computer-readable storage medium as described below to enable the general-purpose processor 502 or the special-purpose processor 504 to perform various functions. The special-purpose processor 504 may be a computing device having hardware or software elements that facilitate the calculation of neural network computing tasks such as training and reasoning calculations. For example, the special-purpose processor 504 may be an accelerator, such as a neural network processing unit ("NPU"), a graphics processing unit ("GPU"), a tensor processing unit ("TPU"), an implementation using a field programmable gate array ("FPGA") and an application-specific integrated circuit ("ASIC"), etc. In order to facilitate the calculation of tasks such as matrix multiplication, the special-purpose processor 504 may, for example, implement an engine that is operable to calculate mathematical operations such as matrix operations and vector operations.

[0114] The system 500 may also include a system memory 506 that is communicatively coupled to the general-purpose processor 502 and the special-purpose processor 504 via a system bus 508. The system memory 506 may be physical or may be virtual and / or distributed. Depending on the exact configuration and type of the system 500, the system memory 506 may be volatile (such as RAM), non-volatile (such as ROM, flash memory, micro hard drive, memory card, etc.), or some combination thereof.

[0115] The system bus 508 can transfer data between the general-purpose processor 502 and the system memory 506, between the special-purpose processor 504 and the system memory 506, and between the general-purpose processor 502 and the special-purpose processor 504. In addition, the data bus 510 can transfer data between the general-purpose processor 502 and the special-purpose processor 504. The data bus 510 can be, for example, a peripheral component interconnect express ("PCIe") connection, a coherent accelerator processor interface ("CAPI") connection, etc.

[0116] Figure 5BAn example of a dedicated processor 504 including any number of cores 512 is illustrated. The processing power of the dedicated processor 504 can be distributed among the cores 512. Each core 512 can include a local memory 514 that can contain pre-initialized data (such as model parameters) or data structures (such as constant buffers for batch normalization or quantization) to perform dedicated calculations. Each core 512 can also be configured to execute one or more sets of computer-executable acceleration engine modules 516 pre-initialized on the local memory 518 of the core 512, and the one or more sets of computer-executable acceleration engine modules 516 can each be executed by the core 512 (including being executed in parallel by multiple cores 512) to, for example, perform or accelerate arithmetic operations such as matrix multiplication or matrix transposition, function operations, or special defined operations such as the MM-ADMM optimized augmented Lagrangian operator described herein. Each core 512 may also include an instruction sequencer 520 that receives and sorts instructions received from an instruction buffer 522. Some number (such as four) of cores 512 may communicate via a data bus 524 (such as a unidirectional ring bus). A software driver that controls the operation of each core 512 may control the core 512 and send executable commands via a command processor interface 526 to synchronize the operation of the core 512.

[0117] The data sequence may be transmitted via the system bus 508 or the data bus 510 to the dedicated processor 504 , wherein the dedicated processor 504 may perform variance change point detection on the data sequence as described herein and output variance change points as described herein.

[0118] Therefore, example embodiments of the present disclosure provide for detecting variance change points of a target time series based on a baseline assumption of statistical stationarity. Example embodiments of the present disclosure provide for removing a trend component signal from a target signal and regularizing the remaining residual component signal using a sparse regularization term. Example embodiments of the present disclosure also provide for an augmented Lagrangian operator and an MM-ADMM method for performing the above two functions. Example embodiments of the present disclosure also provide for calculating a centralized cumulative sum based on the residual component signal and determining a variance change point based on the centralized cumulative sum. For example, the application of a sparse regularization term and a centralized cumulative sum has been experimentally determined to produce better output than known techniques.

[0119] The variance change points output by the detection method applied to the time series trend model according to the example implementation of the present disclosure can be applied to practical problems, such as monitoring distributed computing, cloud computing, machine learning, data centers, financial systems, e-commerce transactions, etc.

[0120] Figure 6An architectural diagram of a server host 600 and a computing host for computing resources and a time series trend model according to an example embodiment of the present disclosure is illustrated. As described above, according to an example embodiment of the present disclosure, a cloud computing system may operate to provide a server host function for hosting computing resources, which is supported by a computing host such as a data center hosting a time series trend model. Therefore, the figure illustrates some possible architectural implementations of the computing device as described above.

[0121] Server host 600 may be implemented on a network 602 of physical or virtual server nodes 604(1), 604(2), ..., 604(N) (where any unspecified server node may be referred to as server node 604) connected via physical or virtual network connections. In addition, network 602 terminates at physical or virtual edge nodes 606(1), 606(2), ..., 606(N) (where any unspecified edge node may be referred to as edge node 606) located at the physical and / or logical edge of network 602. Edge nodes 606(1)-606(N) may be connected to any number of end devices 608(1), 608(2), ..., 608(N) (where any unspecified end device may be referred to as end device 608).

[0122] A time series trend model 610 implemented on a computing host accessed through an interface of a server host 600 as described in an example embodiment of the present disclosure may be stored on a physical or virtual memory ("computing host memory 614") of a computing host 612 and may be loaded into a physical or virtual storage ("computing host storage 616") of the computing host 612 so that one or more physical or virtual processors ("computing host processors (618)") of the computing host 612 perform calculations using the time series trend model 610 to calculate time series data related to optimization as described herein. The computing host processor 618 may be a dedicated computing device that facilitates the calculation of matrix arithmetic calculation tasks. For example, the computing host processor 618 may be one or more dedicated processors 504 as described above, including accelerators such as neural network processing units ("NPUs"), graphics processing units ("GPUs"), tensor processing units ("TPUs"), and the like.

[0123] According to an exemplary embodiment of the present disclosure, Figure 7 Different modules of the described time series trend model may be executed by different processors of the computing host processor 618, or may be executed by the same processor of the computing host processor 618 on different cores or different threads, and each module may perform calculations concurrently with respect to each other sub-module.

[0124] Figure 7An example computing system 700 for implementing the above-described processes and methods for implementing variance change point detection is illustrated.

[0125] The techniques and mechanisms described herein may be implemented by multiple instances of computing system 700, as well as by any other computing device, system, and / or environment. Computing system 700 may be any kind of computing device, such as a personal computer, a personal tablet, a mobile device, other such computing device operable to perform matrix arithmetic calculations. Figure 7 The computing system 700 shown is only one example of a system and is not intended to imply any limitation on the scope of use or functionality of any computing device used to perform the above-described processing and / or processes. Other well-known computing devices, systems, environments, and / or configurations that may be suitable for use with the embodiments include, but are not limited to, personal computers, server computers, handheld or laptop devices, multiprocessor systems, microprocessor-based systems, set-top boxes, game consoles, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above-described systems or devices, implementations using field programmable gate arrays ("FPGAs") and application-specific integrated circuits ("ASICs"), and the like.

[0126] The system 700 may include one or more processors 702 and system storage 704 connected to the processor 702 in a communicative manner. The processor 702 and the system storage 704 may be physical, or may be virtual and / or distributed. The processor 702 may execute one or more modules and / or processes to enable the processor 702 to perform various functions. In an embodiment, the processor 702 may include a central processing unit ("CPU"), a GPU, an NPU, a TPU, any combination thereof, or other processing units or components known in the art. In addition, each processor in the processor 702 may have its own local storage, which may also store program modules, program data, and / or one or more operating systems.

[0127] System storage 704 may be volatile (such as RAM), non-volatile (such as ROM, flash memory, micro hard drive, memory card, etc.), or some combination thereof, depending on the exact configuration and type of computing system 700. System storage 704 may include one or more computer executable modules 706 that may be executed by processor 702. Module 706 may be hosted on a network as a service for a data processing platform that may be implemented on a separate system from computing system 700.

[0128] Module 706 may include, but is not limited to, a trend component removal module 708, a variance filtering module 710, and a change point location module 712. The trend component removal module 708 may further include a target signal acquisition submodule 714, a trend removal cost function optimization submodule 716, and a trend component subtraction submodule 718. The variance filtering module 710 may further include a residual component square submodule 720 and a variance filtering cost function optimization submodule 722. The change point location module 712 may further include a cumulative sum calculation submodule 724, a centralized cumulative sum calculation submodule 726, and a segmentation submodule 728.

[0129] The target signal acquisition submodule 714 may be configured to acquire a target signal of a target time series, as described above with reference to step 202 .

[0130] The trend removal cost function optimization submodule 716 may be configured to optimize the signal cost function for the target signal to output a trend component signal of the target signal, as described above with reference to step 204 .

[0131] The trend component subtraction submodule 718 may be configured to subtract the trend component signal from the target signal to obtain a residual component signal of the target signal, as described above with reference to step 206 .

[0132] The residual component squaring submodule 720 may be configured to square the residual component signal of the target signal, as described above with reference to step 302 .

[0133] The variance filtering cost function optimization submodule 722 may be configured to optimize the signal cost function for the residual component signal to output an estimated variance of the residual component signal, as described above with reference to step 304 .

[0134] The cumulative sum calculation submodule 724 may be configured to calculate a cumulative sum of the estimated variance of the residual component signal over time, as described above with reference to step 402 .

[0135] The centralized cumulative sum calculation submodule 726 may be configured to calculate a centralized cumulative sum based on the cumulative sum, as described above with reference to step 404 .

[0136] The segmentation module 728 may be configured to segment the centered cumulative sum to generate variance change points of the centered cumulative sum, as described above with reference to step 406 .

[0137] The system 700 may additionally include an input / output ("I / O") interface 740 and a communication module 750 that allow the system 700 to communicate with other systems and devices (such as, for example, a server host as described above) over a network. The network may include the Internet, wired media such as a wired network or a direct wired connection, and wireless media such as acoustic, radio frequency ("RF"), infrared, and other wireless media.

[0138] Some or all of the operations of the above methods may be performed by executing computer-readable instructions stored on a computer-readable storage medium as defined below. The term "computer-readable instructions" as used in the specification and claims includes routines, applications, application modules, program modules, programs, components, data structures, algorithms, etc. Computer-readable instructions may be implemented on a variety of system configurations, including single-processor or multi-processor systems, minicomputers, mainframe computers, personal computers, handheld computing devices, microprocessor-based programmable consumer electronics, combinations thereof, and the like.

[0139] Computer-readable storage media may include volatile memory, such as random access memory ("RAM"), and / or non-volatile memory, such as read-only memory ("ROM"), flash memory, etc. Computer-readable storage media may also include additional removable and / or non-removable memory, including but not limited to flash memory, magnetic memory, optical memory, and / or tape memory that can provide non-volatile storage of computer-readable instructions, data structures, program modules, etc.

[0140] Non-temporary computer-readable storage media are examples of computer-readable media. Computer-readable media include at least two types of computer-readable media, namely, computer-readable storage media and communication media. Computer-readable storage media include volatile and non-volatile, removable and non-removable media implemented with any processing or technology for storing information such as computer-readable instructions, data structures, program modules or other data. Computer-readable storage media include, but are not limited to, phase change memory ("PRAM"), static random access memory ("SRAM"), dynamic random access memory ("DRAM"), other types of random access memory ("RAM"), read-only memory ("ROM"), electrically erasable programmable read-only memory ("EEPROM"), flash memory or other memory technology, compact disc read-only memory ("CD-ROM"), digital versatile disk ("DVD") or other optical memory, cassette, tape, disk storage or other magnetic storage device, or any other non-transmission medium that can be used to store information for access by a computing device. In contrast, communication media can embody computer-readable instructions, data structures, program modules or other data in a modulated data signal or other transmission mechanism such as a carrier wave. As defined herein, computer-readable storage media do not include communications media.

[0141] The computer readable instructions stored on one or more non-transitory computer readable storage media, when executed by one or more processors, may perform the above-referenced Figures 1 to 4 Typically, computer-readable instructions include routines, programs, objects, components, data structures, etc. that perform specific functions or implement specific abstract data types. The order in which the operations are described is not intended to be construed as limiting, and any number of the described operations may be combined in any order and / or in parallel to implement the described process.

[0142] The performance of variance change point detection according to the example embodiments of the present disclosure was measured against a variety of variance change point detection methods implemented in the library of the industry standard statistical analysis software development tool R as known in the art. These methods are implemented in R's change point ("cpt") library (called by a function call to "cpt.var") and R's multiple change point detection ("wbs") library (called by a function call to "wbs"). These methods include:

[0143] The Pruned Exact Linear Time ("PELT") algorithm by Killick, Fearnhead, and Eckley;

[0144] The Cumulative Sum of Squares (“CSS”) algorithm proposed by Inclan and Tiao; and

[0145] The Wild Binary Segmentation ("wbs.lsw") algorithm proposed by Korkas and Fryzlewiez.

[0146] Synthetic time series data sets were generated to include 1600 data points each with randomly generated noise, multiple randomly generated anomalies, and a trend that exhibited non-stationarity such that the variance varied three times per time series. FIG. 8A to FIG. 8D An example of a synthetic time series is illustrated.

[0147] Fig. 8A The generated synthetic signal is illustrated, having three variance change points (illustrated by vertical dashed lines) and noise, but having no anomalies and having a trend exhibiting stationarity.

[0148] Figure 8B Demonstrates randomly generated exceptions and inserts Fig. 8A A non-stationary trend signal is generated by the signal.

[0149] Figure 8C Example of inserting Figure 8B After the abnormal Fig. 8A signal.

[0150] Fig.8D Example of inserting Figure 8B After the trend signal Figure 8C signal.

[0151] The performance of each model is measured based on the relaxed precision (“pr”), recall (“re”), and F1 score (“f1”) given in Table 2 below (where, in each case, the closer the score is to 1, the better the performance).

[0152]

[0153] It can be seen that the variance change point detection method ("proposed robust CoV") according to the example implementation of the present disclosure generally outperforms various other methods in the case where anomalies, trend signals, and both anomalies and trend signals are added to the synthetic signal. Specifically, in the case of adding a trend signal, the method according to the example implementation of the present disclosure significantly outperforms PLET and CSS due to the performance of trend removal and sparse regularization. In addition, although wbs.lsw performs better than both PLET and CSS in those cases, the method according to the example implementation of the present disclosure is still better than wbs.lsw due to the performance of centralized accumulation and subsequent segmentation (which is not available in various known methods).

[0154] In addition, the dataset released by Laptev, Amizadeh, and Flint of Yahoo! in 2015 was also used to test various methods. In this case, since the true variance change points are known, the following Table 3 gives the variance change point detections of various corresponding methods relative to the true variance change points (where applicable, the detection point closest to the true point is highlighted).

[0155]

[0156] Again, it can be seen that the method according to the example embodiment of the present disclosure performs best.

[0157] Through the above technical scheme, the present disclosure provides a method for detecting variance change points of a target time series based on a baseline assumption of statistical stationarity. The target time series signal is modeled as including a trend component signal and a residual component signal. For the target signal, a signal cost function including at least a difference penalty function and at least one regularization term is optimized to output the trend component signal of the target signal. For the residual component signal, a signal cost function including at least a difference penalty function and at least one regularization term is optimized to output the estimated variance of the residual component signal. The two signal cost functions can be optimized by optimizing the augmented Lagrangian operator. The centralized cumulative sum is calculated based on the cumulative sum of the estimated variance. The centralized cumulative sum is segmented to generate the variance change point of the centralized cumulative sum. At least due to the removal of the trend component signal and the sparse regularization term used to optimize the signal cost function and the segmentation of the centralized cumulative sum to directly detect the variance change point, the method of the present disclosure provides improved performance compared to the existing methods.

[0158] Sample Clauses

[0159] A. A variance change point detection method, which includes the following steps: optimizing a variance filtering signal cost function for a residual component signal of a target signal of a time series to output an estimated variance of the residual component signal; calculating a time-centered cumulative sum of the estimated variance of the residual component signal; and segmenting the centralized cumulative sum to generate one or more variance change points of the target signal.

[0160] B. According to the variance change point detection method recorded in paragraph A, the variance change point detection method further includes the following steps: for the target signal, optimizing the trend removal signal cost function to output the trend component signal of the target signal; wherein the residual component signal is obtained by subtracting the difference of the trend component signal from the target signal.

[0161] C. The variance change point detection method according to paragraph B, wherein the residual component signal is obtained by further squaring the difference obtained by subtracting the trend component signal from the target signal.

[0162] D. According to the variance change point detection method described in paragraph B, each of the trend removal signal cost function and the variance filtering signal cost function includes at least a difference penalty function and at least one regularization term.

[0163] E. A variance change point detection method according to paragraph D, wherein each difference penalty function comprises a Huber loss function.

[0164] F. A variance change point detection method according to paragraph D, wherein at least one of the respective regularization terms comprises a sparse regularization term.

[0165] G. According to the variance change point detection method described in paragraph B, the step of optimizing the trend removal signal cost function and the step of optimizing the variance filtering signal cost function respectively include optimizing the augmented Lagrangian operator.

[0166] H. A variance change point detection system, the variance change point detection system comprising: one or more processors; and a storage device, the storage device being communicatively connected to the one or more processors, the storage device storing computer executable modules that can be executed by the one or more processors, and when executed by the one or more processors, the computer executable modules performing associated operations, the computer executable modules comprising: a variance filtering module, the variance filtering module further comprising a variance filtering cost function optimization module, the variance filtering cost function optimization module being configured to optimize the variance filtering signal cost function for a residual component signal of a target signal of a time series to output an estimated variance of the residual component signal; and a change point positioning module, the change point positioning module further comprising: a centralized cumulative sum calculation submodule, the centralized cumulative sum calculation submodule being configured to calculate the centralized cumulative sum of the estimated variance of the residual component signal in time; and a segmentation submodule, the segmentation submodule being configured to segment the centralized cumulative sum to generate one or more variance change points of the target signal.

[0167] I. According to the variance change point detection system recorded in paragraph H, the variance change point detection system further includes a trend component removal module, and the trend component removal module further includes: a trend removal cost function optimization submodule, the trend removal cost function optimization submodule is configured to optimize the trend removal signal cost function for the target signal to output the trend component signal of the target signal; and a trend component subtraction submodule, the trend component subtraction submodule is configured to obtain the residual component signal by subtracting the difference of the trend component signal from the target signal.

[0168] J. A variance change point detection system according to paragraph I, wherein the variance filtering module further comprises a residual component square submodule, and the residual component square submodule is configured to square the difference obtained by subtracting the trend component signal from the target signal.

[0169] K. A variance change point detection system according to paragraph I, wherein the trend removal signal cost function and the variance filtering signal cost function respectively include at least a difference penalty function and at least one regularization term.

[0170] L. A variance change point detection system according to paragraph K, wherein each difference penalty function includes a Huber loss function.

[0171] M. A variance change point detection system according to paragraph K, wherein at least one of the respective regularization terms comprises a sparse regularization term.

[0172] N. A variance change point detection system according to paragraph I, wherein the trend removal cost function optimization submodule and the variance filtering cost function optimization submodule are configured to respectively optimize the trend removal signal cost function and the variance filtering signal cost function by optimizing the augmented Lagrangian operator.

[0173] O. A computer-readable storage medium, which stores computer-readable instructions that can be executed by one or more processors. When executed by the one or more processors, the computer-readable instructions cause the one or more processors to perform operations, the operations including: optimizing a variance filtering signal cost function for a residual component signal of a time series target signal to output an estimated variance of the residual component signal; calculating a time-centered cumulative sum of the estimated variance of the residual component signal; and segmenting the centralized cumulative sum to generate one or more variance change points of the target signal.

[0174] P. According to the computer-readable storage medium recorded in paragraph O, the operation further includes: optimizing the trend removal signal cost function for the target signal to output the trend component signal of the target signal; wherein the residual component signal is obtained by subtracting the difference between the trend component signal and the target signal.

[0175] Q. The computer-readable storage medium of paragraph P, wherein the residual component signal is obtained by further squaring the difference of subtracting the trend component signal from the target signal.

[0176] R. A computer-readable storage medium according to paragraph P, wherein the trend removal signal cost function and the variance filtering signal cost function respectively include at least a difference penalty function and at least one regularization term.

[0177] S. A computer-readable storage medium according to paragraph R, wherein the respective difference penalty functions include a Huber loss function.

[0178] T. A computer-readable storage medium as described in paragraph R, wherein the respective at least one regularization term includes a sparse regularization term.

[0179] U. A computer-readable storage medium according to paragraph P, wherein each of the steps of optimizing the trend removal signal cost function and optimizing the variance filtering signal cost function comprises optimizing an augmented Lagrangian operator.

[0180] Although the subject matter has been described in language specific to structural features and / or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described. Rather, the specific features and acts are disclosed as example forms of implementing the claims.

Claims

1. A variance change point detection method, the variance change point detection method comprising the following steps: For the residual component signal of the target signal of the time series, optimizing the variance filtering signal cost function to output the estimated variance of the residual component signal; Calculating a time-centered cumulative sum of the estimated variance of the residual component signal; Segmenting the centered cumulative sum to generate one or more variance change points of the target signal; as well as For the target signal, optimizing the trend removal signal cost function to output a trend component signal of the target signal, The residual component signal is obtained by subtracting the trend component signal from the target signal.

2. The variance change point detection method according to claim 1, wherein: The residual component signal is obtained by further squaring the difference of subtracting the trend component signal from the target signal.

3. The variance change point detection method according to claim 1, wherein: Each of the trend removal signal cost function and the variance filtering signal cost function includes at least a difference penalty function and at least one regularization term, respectively.

4. The variance change point detection method according to claim 3, wherein: The respective difference penalty functions include the Huber loss function.

5. The variance change point detection method according to claim 3, wherein: The respective at least one regularization term comprises a sparse regularization term.

6. The variance change point detection method according to claim 1, wherein: The step of optimizing the trend removal signal cost function and the step of optimizing the variance filtering signal cost function respectively include optimizing the augmented Lagrangian operator.

7. A variance change point detection system, the variance change point detection system comprising: one or more processors; as well as A storage device is communicatively coupled to the one or more processors, the storage device storing computer executable modules executable by the one or more processors, and when executed by the one or more processors, the computer executable modules perform associated operations, the computer executable modules comprising: A variance filtering module, the variance filtering module further comprising a variance filtering cost function optimization module, the variance filtering cost function optimization module being configured to optimize the variance filtering signal cost function for the residual component signal of the target signal of the time series, so as to output an estimated variance of the residual component signal; A change point positioning module, the change point positioning module further comprises: a centralized cumulative sum calculation submodule, the centralized cumulative sum calculation submodule being configured to calculate a centralized cumulative sum of the estimated variance of the residual component signal in time, and A segmentation submodule, the segmentation submodule is configured to segment the centralized cumulative sum, to generate one or more variance change points of the target signal; a trend removal cost function optimization submodule, wherein the trend removal cost function optimization submodule is configured to optimize a trend removal signal cost function for the target signal to output a trend component signal of the target signal; and A trend component subtraction submodule is configured to obtain the residual component signal by subtracting a difference of the trend component signal from the target signal.

8. The variance change point detection system according to claim 7, wherein: The variance filter module further includes a residual component square submodule configured to square the difference of subtracting the trend component signal from the target signal.

9. The variance change point detection system according to claim 7, wherein: The trend removal signal cost function and the variance filtering signal cost function respectively include at least a difference penalty function and at least one regularization term.

10. The variance change point detection system according to claim 9, wherein: The respective difference penalty functions include the Huber loss function.

11. The variance change point detection system according to claim 9, wherein: The respective at least one regularization term comprises a sparse regularization term.

12. The variance change point detection system according to claim 7, wherein: The trend removal cost function optimization submodule and the variance filtering cost function optimization submodule are configured to optimize the trend removal signal cost function and the variance filtering signal cost function, respectively, by optimizing an augmented Lagrangian operator.

13. A computer-readable storage medium storing computer-readable instructions executable by one or more processors, wherein when executed by the one or more processors, the computer-readable instructions cause the one or more processors to perform operations, the operations comprising: For the residual component signal of the target signal of the time series, optimizing the variance filtering signal cost function to output the estimated variance of the residual component signal; Calculating a time-centered cumulative sum of the estimated variance of the residual component signal; Segmenting the centered cumulative sum to generate one or more variance change points of the target signal; as well as For the target signal, optimizing the trend removal signal cost function to output a trend component signal of the target signal, The residual component signal is obtained by subtracting the trend component signal from the target signal.

14. The computer-readable storage medium of claim 13, wherein: The residual component signal is obtained by further squaring the difference of subtracting the trend component signal from the target signal.

15. The computer-readable storage medium of claim 13, wherein: The trend removal signal cost function and the variance filtering signal cost function respectively include at least a difference penalty function and at least one regularization term.

16. The computer-readable storage medium of claim 15, wherein: The respective difference penalty functions include the Huber loss function.

17. The computer-readable storage medium of claim 15, wherein: The respective at least one regularization term comprises a sparse regularization term.

18. The computer-readable storage medium of claim 13, wherein: The operation of optimizing the trend removal signal cost function and the operation of optimizing the variance filtering signal cost function respectively include optimizing the augmented Lagrangian operator.

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