Aggregate Markov model dimension reduction method and device for dynamic system monitoring
By constructing an intermediate matrix and using a bipartite graph maximum matching algorithm, the dimensionality reduction problem of aggregated Markov models under non-stationary initial conditions is solved, achieving efficient computation and state prediction in dynamic systems.
Patent Information
- Application Number
- CN202511886382.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-15
- Publication Date
- 2026-03-17
AI Technical Summary
Existing aggregated Markov models rely heavily on the assumption of stationary initial distribution, which cannot adapt to non-stationary initial conditions in dynamic systems. This leads to a mismatch between theoretical premises and practical application scenarios, and there is a lack of dimensionality reduction methods to handle non-stationary initial conditions.
By constructing an intermediate matrix and using the bipartite graph maximum matching algorithm, it is determined whether the aggregated Markov model can be dimensionality reduced. If it can be dimensionality reduced, a dimensionality reduction transformation matrix is constructed to generate an equivalent model with lower dimensionality.
It enables automatic dimensionality reduction and model building under non-stationary initial conditions, reducing computational complexity and improving computational efficiency. It is suitable for real-time state prediction of edge devices with limited computing power.
Smart Images
Figure CN121682115A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of model optimization, in particular to a dimension reduction method and device of an aggregated Markov model for dynamic system monitoring. BACKGROUND
[0002] An aggregated Markov model is a special kind of hidden Markov model, and its core feature is that each hidden state corresponds to a fixed observation value, and the observation matrix only contains binary elements. An aggregated Markov model can be represented by a probability transition matrix , an observation probability matrix and an initial distribution vector . Wherein, is a matrix of , is a matrix of , is a vector of , is the dimension of the aggregated Markov model, is the number of observation variables. In the aggregated Markov model, the observation probability matrix . Define is a diagonal matrix generated by the row elements of the observation probability matrix . The probability of the aggregated Markov model generating a sequence can be expressed as
[0003]
[0004] Where is a vector with all elements being 1. Two different aggregated Markov models may have the same observation probability for all possible observation sequences, so they cannot be distinguished from the observation sequence, and they can be replaced with each other from the perspective of observation sequence probability value calculation. Using an aggregated Markov model with a lower dimension as a mathematical model can effectively reduce the computational complexity, save the calculation cost, and improve the numerical calculation efficiency.
[0005] The existing technology only targets stationary initial conditions, i.e. is This paper proposes a dimensionality reduction modeling algorithm based on the eigenvector premise. Real-world models commonly exhibit non-stationary conditions. For example, in epidemiology (such as the SEIR model), hidden states represent susceptible individuals, exposed individuals, infected individuals, and recovered individuals in a population. However, the actual population composition in the early stages of an epidemic (such as a high proportion of susceptible individuals) often needs to be represented by a non-stationary distribution. In protein evolution research, when the hidden state is a genetic codon and the observed value is the corresponding amino acid, if a specific amino acid is initially observed, the initial distribution must assign a non-zero probability to the corresponding codon (the probability of other codons is zero). This requirement directly violates the stationarity assumption. This disconnect between theoretical premise and practical application leads to two major bottlenecks: first, the stationarity requirement cannot adapt to the diversity of initial states in dynamic systems (such as epidemic outbreaks or biological evolution); second, existing methods for judging dimensionality reduction (such as spectral decomposition) are limited to stationary scenarios and lack universal algorithms for handling non-stationary initial conditions. There is an urgent need to establish a systematic method for judging the dimensionality reduction of aggregate Markov models under non-stationary initial conditions and a dimensionality reduction modeling method. Summary of the Invention
[0006] In view of this, the purpose of this invention is to propose a method and apparatus for dimensionality reduction of aggregated Markov models for dynamic system monitoring, in order to solve the problem that the realization problem of existing aggregated Markov models (AMM) strictly depends on the assumption of stationary initial distribution, but the actual initial conditions of dynamic systems generally exhibit non-stationary characteristics, resulting in a mismatch between theoretical premises and real application scenarios.
[0007] To achieve the above objectives, this invention provides a method for dimensionality reduction of aggregated Markov models for dynamic system state monitoring, comprising the following steps:
[0008] Step S1: Obtain the n×n-dimensional probability transition matrix Q, the d×n-dimensional observation probability matrix O, and the n×1-dimensional initial distribution vector p of the target aggregated Markov model after dimensionality reduction;
[0009] Step S2: Based on the observation probability matrix O, generate d n×n dimensional diagonal matrices. Where i represents the i-th observation category, i.e., the matrix The kth diagonal element is the element in the i-th row and k-th column of the observation probability matrix O;
[0010] Step S3: Construct an intermediate matrix based on the diagonal matrix, the probability transition matrix Q, and the initial distribution vector p. ;
[0011] Step S4: Based on the intermediate matrix Construct the first bipartite graph and calculate its maximum matching number. Based on the maximum number of matches Based on the relationship between the size of the model dimension n, determine whether the aggregated Markov model can be reduced in dimensionality;
[0012] Step S5: If it is determined that the dimension can be reduced, then for each observation category i, based on the sub-matrix block in the intermediate matrix M... Calculate the corresponding transformation submatrix and by all Combined to form an n×m dimensional transformation matrix , where m <n;
[0013] Step S6: Based on the transformation matrix and its left inverse matrix Construct a dimension-m reduced aggregated Markov model, wherein the dimension-m reduced aggregated Markov model is composed of a dimension-reduced probability transition matrix. , dimensionality reduction observation matrix and the initial distribution vector for dimensionality reduction definition.
[0014] Preferably, in step S4, determining whether the aggregated Markov model can be dimensionality reduced includes:
[0015] like If n < n, then the aggregated Markov model is determined to be dimensionality-reducible; otherwise, it is determined to be dimensionality-reducible.
[0016] Preferably, in step S5, the corresponding transformation submatrix is calculated. The steps include:
[0017] Step S51: Obtain the number of elements with a value of 1 in the i-th row of the observation probability matrix O. ;
[0018] Step S52: Construct a matrix The second bipartite graph with the left vertex as its left vertex and its column as its right vertex. And calculate its maximum number of matches. and the maximum matching vector Maximum matching vector The Middle The element represents the leftmost element. The index of the right vertex corresponding to each vertex;
[0019] Step S53: If equal Then, from the diagonal matrix All non-zero columns form the transformation submatrix ;
[0020] Step S54: If Less than Then from the matrix The maximum matching vector is in The specified columns constitute the transformation submatrix .
[0021] Preferably, in step S5, an n×m dimensional transformation matrix is formed. Afterwards, Each column vector in the data is normalized.
[0022] Preferably, the dynamic system is a 5G or 6G mobile communication network, the state is the connection quality status of the network node, and the observation is an indicator of the availability of the network connection.
[0023] This invention also provides a dynamic system state monitoring aggregation Markov model dimensionality reduction system, comprising:
[0024] The data acquisition module is used to obtain the performance parameters of the dynamic system;
[0025] The data acquisition module is used to obtain the performance parameters of the target aggregated Markov model dimensionality reduction.
[0026] The model processing module is used to construct an initial aggregated Markov model based on the performance parameters, and to obtain a dimension-reduced aggregated Markov model using the dimensionality reduction method described above.
[0027] The state prediction module is used to predict the future state of the dynamic system based on the dimensionality reduction model.
[0028] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described aggregate Markov model dimensionality reduction method.
[0029] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described aggregate Markov model dimensionality reduction method.
[0030] The beneficial effects of this invention are:
[0031] 1. This invention provides a clear and computable mathematical criterion by constructing a specific intermediate matrix and using a bipartite graph maximum matching algorithm. This criterion can automatically and reliably determine whether an aggregated Markov model with any given non-stationary initial conditions can be reduced in dimensionality.
[0032] 2. For models that can be reduced in dimensionality, this invention can automatically construct an accurate transformation matrix and generate a lower-dimensional aggregated Markov model. This reduced-dimensional model, given the same input observation sequence, can produce an output that is completely equivalent to the original model in terms of probability distribution. Because the model's state dimension is reduced, the dimensionality of the core operations involved in state decoding, prediction, or likelihood calculation is also reduced, thereby directly and significantly reducing the number of floating-point operations and memory storage overhead required for computation, and improving computational efficiency.
[0033] 3. The dimensionality reduction effect achieved by the method of this invention is of key significance for deploying complex state monitoring models on edge devices (such as 5G base stations and IoT gateways) where computing power, storage space, and power consumption are limited. This makes it easier to implement real-time or near-real-time state prediction and fault early warning in the embedded processing unit of the base station, providing a feasible technical path for network autonomy.
[0034] 4. This invention can handle more general cases where the initial state is non-uniformly distributed. The resulting dimensionality reduction model is equivalent to the original model not only in terms of long-term statistical properties, but also in terms of short-term prediction behavior starting from a specific initial state. Therefore, it has wider applicability and higher practicality. Attached Figure Description
[0035] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0036] Figure 1 This is a flowchart of the dimensionality reduction method for aggregated Markov models in dynamic system monitoring according to an embodiment of the present invention. Detailed Implementation
[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.
[0038] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.
[0039] Example 1:
[0040] The realization problem of existing aggregated Markov models (AMMs) strictly relies on the assumption of a stationary initial distribution. However, the actual initial conditions of dynamic systems (such as the proportion of susceptible people in the early stage of an epidemic or the initial observation of specific amino acids in protein evolution) generally exhibit non-stationary characteristics, leading to a mismatch between theoretical premises and real-world application scenarios.
[0041] To address this, this embodiment provides a method for dimensionality reduction of aggregated Markov models for dynamic system monitoring, such as... Figure 1 As shown, it includes the following steps:
[0042] Step S1: Obtain the parameters of the target aggregated Markov model: Obtain the three core parameters of the aggregated Markov model to be reduced in dimensionality: the n×n probability transition matrix Q, the d×n observation probability matrix O, and the n×1 initial distribution vector p. Here, n represents the total number of hidden states in the model, and d represents the total number of observation categories in the system.
[0043] Step S2: Generate the observation diagonal matrix: Based on the observation probability matrix O, generate a corresponding diagonal matrix for each observation category. Specifically, for the i-th observation category (i=1,…,d), generate an n×n dimensional diagonal matrix. The matrix The kth diagonal element is equal to the element in the i-th row and k-th column of the observation probability matrix O.
[0044] Step S3: Construct intermediate matrices: Using all the diagonal matrices generated in step S2 Given the probability transition matrix Q and the initial distribution vector p, construct an intermediate matrix M. This matrix M is constructed by combining two sub-matrix blocks corresponding to each observation class i. Horizontally spliced in the order of i, and its mathematical expression is: This matrix synthesizes the dynamic and initial information of the model under all observation conditions.
[0045] Step S4: Dimensionality reduction determination based on bipartite graph matching: Based on the intermediate matrix M, construct a first bipartite graph B. The left vertex set of this bipartite graph corresponds to the n states of the model, and the right vertex set corresponds to each column of the intermediate matrix M. By calculating the maximum matching number of this bipartite graph B and comparing it with the model dimension n to determine whether the model can be dimensionally reduced. The specific determination rule is: If the maximum matching number is less than the model dimension n, it is determined that the aggregated Markov model can be dimensionally reduced; otherwise, it is determined that it cannot be dimensionally reduced.
[0046] Step S5: Construct a dimensionality reduction transformation matrix: If it is determined in step S4 that the model can be dimensionally reduced, then for each observation category i, perform the following operations to construct a transformation sub-matrix :
[0047] S51: Obtain the number of elements with a value of 1 in the i-th row of the observation probability matrix O .
[0048] S52: For the sub-matrix block corresponding to this observation category in the intermediate matrix M , construct a second bipartite graph . The left vertex set of this graph corresponds to the rows of the sub-matrix block, and the right vertex set corresponds to its columns. Calculate the maximum matching number of this bipartite graph and the maximum matching vector .Each column is normalized.
[0052] Step S6: Generate a dimensionality reduction model: based on the transformation matrix obtained in step S5. and its left inverse matrix We construct a new aggregated Markov model of dimension m, i.e., a dimensionality-reduced model. This dimensionality-reduced model is defined by the following parameters: the dimensionality reduction probability transition matrix. , dimensionality reduction observation matrix and the initial distribution vector for dimensionality reduction This dimensionality reduction model is equivalent to the original model in terms of the probability distribution of the observation sequence, but has lower computational complexity.
[0053] Example 2:
[0054] The 5G base station connectivity monitoring system can be modeled using an aggregated Markov model. There are a total of 6 hidden states: High-quality connection status. Medium quality connection status, Interruption recovery status, Congestion recovery status. Anti-interference state, Offline status. Probability transition matrix. The element in the i-th row and j-th column represents the state. to state The transition probability. Where, state... and Corresponding observation status Connection available, status and Corresponding observation status Connection unavailable. Initially, there was a 79.8% probability of a high-quality connection. 20.2% probability of being a medium-quality connection Based on the above, the probability transition matrix... Observation probability matrix Initial distribution vector As shown below:
[0055] .
[0056] The maximum number of matching solutions proposed The model can be dimensionality reduced. (Bipartite graph) Maximum number of matches Bipartite graph Maximum number of matches The maximum matching vector is The transformation matrix and dimensionality reduction model are as follows:
[0057]
[0058] Using the proposed technical solution, this model can be reduced to a dimensionless form. Furthermore, the dimensionality reduction model is equivalent to the original model in terms of observation state detection. When the dimensionality reduction model is used to predict the future available state of the network, it can effectively reduce computational complexity, save computational costs, and improve numerical computation efficiency.
[0059] Example 3:
[0060] This embodiment provides a dynamic system state monitoring aggregated Markov model dimensionality reduction system, including:
[0061] The data acquisition module is used to obtain the performance parameters of the dynamic system;
[0062] The data acquisition module is used to obtain the performance parameters of the target aggregated Markov model dimensionality reduction.
[0063] The model processing module is used to construct an initial aggregated Markov model based on the performance parameters, and to obtain a dimension-reduced aggregated Markov model using the dimension reduction method described in any one of claims 1-5.
[0064] The state prediction module is used to predict the future state of the dynamic system based on the dimensionality reduction model.
[0065] Example 4:
[0066] This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aggregated Markov model dimensionality reduction method as described in Embodiment 1.
[0067] Example 5:
[0068] This embodiment provides a computer-readable storage medium storing a computer program, which, when executed by a processor, represents the dimensionality reduction method of the aggregated Markov model in Embodiment 1.
[0069] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.
[0070] In the embodiments provided in this application, it should be understood that the disclosed devices / terminal equipment and methods can be implemented in other ways. For example, the device / terminal equipment embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling or direct coupling or communication connection may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.
[0071] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.
[0072] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.
[0073] The implementation of all or part of the processes in the methods of the above embodiments can also be accomplished by a computer program product. When the computer program product is run on a terminal device, the terminal device can implement the steps in the various method embodiments described above.
[0074] The embodiments described above are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.
Claims
1. A method for dimensionality reduction of aggregated Markov models for dynamic system state monitoring, characterized in that, The method comprises the following steps: In step S1, an n*n-dimensional probability transition matrix Q, a d*n-dimensional observation probability matrix O and an n*1-dimensional initial distribution vector p of the target aggregated Markov model dimension reduction are obtained. Step S2: Based on the observation probability matrix O, generate d n x n dimensional diagonal matrices where i represents the i-th observation class, i.e. the k-th diagonal element of the matrix is the element of the i-th row and k-th column of the observation probability matrix O. Step S3: Based on the diagonal matrix, the probability transition matrix Q and the initial distribution vector p, an intermediate matrix is constructed ; Step S4: constructing a first bipartite graph based on the intermediate matrix , constructing a first bipartite graph and calculating the maximum matching number thereof , determining whether the aggregated Markov model can be reduced in dimension based on the maximum matching number , determining whether the aggregated Markov model can be reduced in dimension based on the size relationship with the model dimension n Step S5: If it is determined that the dimensionality can be reduced, then for each observation class i, a corresponding transformation sub-matrix is calculated based on the sub-matrix block in the intermediate matrix M, and all are combined to form a transformation matrix of n x m dimensions, where m < n. Step S6: constructing a reduced dimension aggregated Markov model of dimension m based on the transformation matrix and its left inverse matrix , the reduced dimension aggregated Markov model being defined by a reduced dimension probability transition matrix , a reduced dimension observation matrix and a reduced dimension initial distribution vector .
2. The method of claim 1, wherein, In step S4, the determination of whether the aggregated Markov model can be dimension reduced comprises: If < n, then it is determined that the aggregated Markov model is dimension-reducible; otherwise, it is determined that the aggregated Markov model is not dimension-reducible.
3. The method of claim 1, wherein, In step S5, the step of calculating the corresponding conversion sub-matrix includes: Step S51, obtain the number of elements with value 1 in the i-th row of the observation probability matrix O ; Step S52, constructing a second subgraph with the left side vertices of the behavior matrix and the right side vertices of the behavior matrix, and calculating the maximum matching number and the maximum matching vector of the second subgraph Step S53: If is equal to then the transformation submatrix is formed by all non-zero columns of the diagonal matrix ; Step S54: If is smaller than , then the transformation submatrix is formed by the columns of the matrix specified by the maximum matching vector .
4. The dynamic system state monitoring aggregated Markov model dimensionality reduction method of claim 3, wherein, In step S5, an n x m dimensional conversion matrix is formed After that, each column vector in the matrix is normalized. After that, each column vector in the matrix is normalized.
5. The method of claim 1, wherein, The dynamic system is a 5G or 6G mobile communication network, the state is a connection quality state of a network node, and the observation is an availability index of network connection.
6. A dynamic system state monitoring aggregated Markov model dimensionality reduction system, characterized by, Comprise: a data acquisition module configured to acquire performance parameters of a dynamic system; a data acquisition module configured to acquire performance parameters of a target aggregated Markov model dimension reduction; a model processing module configured to construct an initial aggregated Markov model according to the performance parameters and obtain a dimension-reduced aggregated Markov model by using the dimension reduction method according to any one of claims 1-5; a state prediction module configured to predict a future state of the dynamic system based on the dimension-reduced model.
7. An electronic device, comprising: The computer program is stored on the computer readable storage medium and is executable on the processor to implement the aggregated Markov model dimension reduction method according to any one of claims 1-5.
8. A computer-readable storage medium, characterized in that, The computer program is stored on the computer readable storage medium and is executable on the processor to implement the aggregated Markov model dimension reduction method according to any one of claims 1-5.