Gaussian mixture model simplification method based on composite 2-Wasserstein distance
Through a three-stage optimization framework based on the composite 2-Wasserstein distance, greedy merging of Gaussian components, optimization weights and global clustering, the computational burden and difference measurement problems of the Gaussian mixture model are solved, and efficient, simple and accurate model simplification is achieved.
Patent Information
- Application Number
- CN202510698275.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-28
- Publication Date
- 2025-09-09
AI Technical Summary
The number of components in the existing Gaussian mixture model grows exponentially during the calculation process, resulting in excessive computational burden. In addition, the traditional KLD-based simplified method cannot accurately characterize the differences when the Gaussian component distributions are similar, affecting the application effect.
A three-stage optimization framework based on composite 2-Wasserstein distance is adopted, including greedy merging, weight optimization and global clustering. The number of Gaussian components is reduced by greedy merging, the weights are optimized using optimal transfer theory, and the cluster centers are optimized through K-Means clustering to construct a simplified Gaussian mixture model.
It effectively reduces the complexity of the model while maintaining the ability to represent data features, solves the problem that traditional methods cannot perform analytical operations and difference measurements when Gaussian components are close, and improves the accuracy and efficiency of model simplicity.
Smart Images
Figure CN120611802A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of machine learning, and in particular to a Gaussian mixture model simplicity method based on a composite 2-Wasserstein distance. Background Art
[0002] In related technologies, Gaussian mixture (GM) models are widely used in fields such as machine learning, data processing, and target tracking, and are often used to construct parameterized representations of complex probability density functions. Since all Gaussian functions form a complete basis system, that is, each Gaussian function can be approximated with arbitrary precision through a Gaussian mixture, making the Gaussian mixture model a powerful tool in these applications. However, in the recursive processing of the probability density function, the number of components in the Gaussian mixture approximation often grows exponentially, resulting in a heavy computational burden. Therefore, after several computational steps, the Gaussian mixture model must be simplified to prevent an excessive number of components. Among existing solutions, the Gaussian mixture reduction method based on the Kullback-Leibler Divergence (KLD) divergence similarity metric is generally used to achieve the reduction of the Gaussian mixture model. The core idea of this solution is to achieve model simplification by minimizing the KLD upper bound between the Gaussian components to be merged. It is currently the most commonly used Gaussian mixture reduction method in the fields of target tracking and signal processing. However, since the KLD between two GM models cannot be calculated analytically, and when the distributions of two Gaussian components are too close, their degree of difference cannot be characterized, this affects its practical application effect.
[0003] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to ordinary technicians in this field. Summary of the Invention
[0004] The present invention provides a Gaussian mixture model simplification method based on composite 2-Wasserstein distance, a computer program product, a storage medium, and an electronic device, which can overcome the defects in the prior art to a certain extent.
[0005] Other features and advantages of the present invention will become apparent from the following detailed description, or may be learned in part by practice of the present invention.
[0006] According to a first aspect of the present invention, a Gaussian mixture model reduction method based on a composite 2-Wasserstein distance is provided, the method comprising:
[0007] Obtaining the original Gaussian mixture model to be processed and the corresponding model processing index data; wherein the model processing index data includes: target component value;
[0008] Using a greedy merging method, the Gaussian components in the original Gaussian mixture model are merged until the number of Gaussian components reaches a target component value, so as to obtain an initial simplified model;
[0009] The initial parsimonious model is weighted optimized based on the optimal transfer theory, so that the weight-optimized initial parsimonious model approaches the original Gaussian mixture model in terms of the composite 2-Wasserstein distance.
[0010] The K-Means clustering method is used to perform global optimization on the initial minimalist model after weight optimization, and the cluster centers of the initial minimalist model are updated to meet the preset clustering iteration conditions to obtain a minimalist mixed Gaussian model.
[0011] In some exemplary embodiments, a greedy merging method is used to merge the Gaussian components in the original Gaussian mixture model until the number of Gaussian components reaches a target component value to obtain an initial simplified model, including:
[0012] Merge any two Gaussian components in the original Gaussian mixture model to obtain multiple pairing solutions;
[0013] Traverse each pairing scheme to select the optimal pairing scheme to merge the Gaussian components, and iterate until the number of Gaussian components reaches the target component value; among them, in the optimal pairing scheme, the 2-Wasserstein distance between the Gaussian mixture model after the Gaussian components are merged and the original Gaussian mixture model is the smallest.
[0014] In some exemplary embodiments, the method further comprises calculating the 2-Wasserstein distance between the two Gaussian mixture models based on the square of the 2-Wasserstein distance between the Gaussian components of the two Gaussian mixture models and the joint probability density distribution of transmission between the Gaussian components of the models.
[0015] In some exemplary embodiments, performing weight optimization on the initial parsimonious model based on optimal transmission theory includes:
[0016] Define a transmission cost matrix; where each element in the transmission cost matrix represents the square of the 2-Wasserstein distance between the Gaussian component of the original Gaussian mixture model and the Gaussian component in the initial simplified model;
[0017] The optimization problem is defined based on the 2-Wasserstein distance between the original Gaussian mixture model and the initial parsimonious model;
[0018] Based on the transmission amount between the Gaussian components of the model, the constraints are configured and the optimization problem is solved to obtain the weight optimization result corresponding to the initial simple model.
[0019] In some exemplary embodiments, a K-Means clustering method is used to perform global optimization on the initial parsimonious model after weight optimization, and the cluster centers of the initial parsimonious model are updated to meet a preset clustering iteration condition to obtain a parsimonious Gaussian mixture model, including:
[0020] The N Gaussian components of the initial parsimonious model after weight optimization are configured as cluster centers;
[0021] Clustering is performed on the M Gaussian components of the original Gaussian mixture model based on N cluster centers;
[0022] The cluster centers are updated based on the distribution results of the Gaussian components until the preset clustering iteration conditions are met to obtain a simplified mixed Gaussian model.
[0023] In some exemplary embodiments, clustering the M Gaussian components of the original Gaussian mixture model based on the N cluster centers includes:
[0024] Calculate the composite 2-Wasserstein distance between each Gaussian component of the original Gaussian mixture model and each cluster center;
[0025] Based on the distance calculation results, the Gaussian components are assigned to the cluster corresponding to the nearest cluster center; wherein each cluster center of the initial parsimonious model is configured with a corresponding cluster.
[0026] In some exemplary embodiments, updating the cluster center based on the distribution result of the Gaussian component includes:
[0027] The parameters of the cluster center are updated using the center of gravity formula corresponding to the 2-Wasserstein distance to achieve the update of the cluster center; the formula includes:
[0028]
[0029] Among them, w k is the weight after merging Gaussian components, μ k is the mean of the Gaussian distribution after merging the Gaussian components, ∑ k is the covariance of the Gaussian distribution after merging the Gaussian components.
[0030] In some exemplary embodiments, the model processing index data includes: model optimization index data defined based on a composite 2-Wasserstein distance;
[0031] The method further comprises:
[0032] Calculating a model distance between the reduced Gaussian mixture model and the original Gaussian mixture model based on a composite 2-Wasserstein distance;
[0033] The model distance is compared with the model optimization index data to obtain a model simplicity evaluation result.
[0034] In some exemplary embodiments, the method further comprises:
[0035] The model processing indicator data is configured according to the corresponding task processing type and application scenario.
[0036] According to a second aspect of the present invention, a computer program product is provided, on which a computer program is stored, and when the computer program is executed by a processor, the Gaussian mixture model reduction method based on the composite 2-Wasserstein distance is implemented.
[0037] According to a third aspect of the present invention, there is provided a storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the Gaussian mixture model reduction method based on the composite 2-Wasserstein distance is implemented.
[0038] According to a fourth aspect of the present invention, there is provided an electronic device, comprising:
[0039] processor; and
[0040] a memory for storing executable instructions of the processor;
[0041] The processor is configured to implement the above-mentioned Gaussian mixture model reduction method based on composite 2-Wasserstein distance when executing the executable instructions.
[0042] The Gaussian mixture model simplification method based on the composite 2-Wasserstein distance provided by the embodiments of the present invention constructs a three-stage optimization framework based on the analyzable composite 2-Wasserstein distance. This framework sequentially performs greedy component merging, dynamic weight optimization, and global clustering optimization on the Gaussian mixture model to achieve model simplification. This method significantly reduces the model complexity while effectively maintaining the ability to represent the original data features. This method solves the model simplification problems of traditional KLD-based methods due to their asymmetry and inability to perform analytical calculations.
[0043] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention. BRIEF DESCRIPTION OF THE DRAWINGS
[0044] The accompanying drawings are incorporated into and constitute a part of this specification, illustrate embodiments consistent with the present invention, and together with the description, serve to explain the principles of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and it is clear that those skilled in the art can derive other drawings based on these drawings without inventive effort.
[0045] Figure 1 A schematic diagram schematically illustrates a Gaussian mixture model reduction method based on a composite 2-Wasserstein distance according to an exemplary embodiment of the present invention;
[0046] Figure 2 A schematic diagram schematically illustrates a process flow of a simplified method for a Gaussian mixture model based on a composite 2-Wasserstein distance according to an exemplary embodiment of the present invention;
[0047] Figure 3 A schematic diagram schematically illustrating a comparison of two-dimensional simulation accuracy of GW2 distance of models simplified by different methods in an exemplary embodiment of the present invention;
[0048] Figure 4 A schematic diagram schematically illustrating a comparison of the four-dimensional simulation accuracy of the GW2 distance of the model simplified by different methods in an exemplary embodiment of the present invention;
[0049] Figure 5 The figure schematically shows the composition of an electronic device in an exemplary embodiment of the present invention. DETAILED DESCRIPTION
[0050] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
[0051] In addition, the accompanying drawings are merely schematic illustrations of the present invention and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the blocks shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.
[0052] In the related art, the existing Gaussian mixture reduction method based on Kullback-Leibler Divergence (KLD) divergence similarity measure, whose core idea is to achieve model simplification by minimizing the KLD upper bound between the Gaussian components to be merged, is the most commonly used Gaussian mixture reduction method in the current target tracking and signal processing fields. However, since the KLD between two GM models cannot be analytically calculated, and when the distributions of the two Gaussian components are relatively close, the probability density ratio approaches 1, that is, This causes the integrand to approach zero, making it impossible to accurately characterize the essential differences in its structure. This insensitivity can easily lead to problems such as target merging and misassociation in scenarios that rely on fine state discrimination, such as radar target tracking, thus limiting its practical application effect.
[0053] In view of the shortcomings and deficiencies of the existing technology, this example embodiment provides a simplified Gaussian mixture model method based on the composite 2-Wasserstein distance. Figure 1 As shown, the Gaussian mixture model simplified method based on the composite 2-Wasserstein distance may specifically include the following steps:
[0054] Step S11, obtaining the original Gaussian mixture model to be processed and the corresponding model processing index data; wherein the model processing index data includes: target component value;
[0055] Step S12, using a greedy merging method, merging the Gaussian components in the original Gaussian mixture model until the number of Gaussian components reaches a target component value, so as to obtain an initial simplified model;
[0056] Step S13, performing weight optimization processing on the initial minimalist model based on the optimal transmission theory, so that the weight-optimized initial minimalist model approaches the original Gaussian mixture model in terms of the composite 2-Wasserstein distance;
[0057] In step S14, the K-Means clustering method is used to perform global optimization processing on the initial minimalist model after weight optimization, and the cluster centers of the initial minimalist model are updated to meet the preset clustering iteration conditions to obtain a minimalist mixed Gaussian model.
[0058] The method proposed in this paper constructs a three-stage optimization framework based on a parseable composite 2-Wasserstein distance. This framework sequentially performs greedy component merging, dynamic weight optimization, and global clustering optimization on a Gaussian mixture model to achieve model simplification. This method significantly reduces model complexity while effectively maintaining the ability to represent the original data features. This method overcomes the model simplification challenges of traditional KLD-based methods due to their asymmetry and inability to perform parse operations. This method is applicable to applications such as radar target tracking, signal processing, and sensor data fusion.
[0059] Below, each step of the Gaussian mixture model reduction method based on the composite 2-Wasserstein distance in this example implementation will be described in more detail with reference to the accompanying drawings and examples.
[0060] In step S11 , the original Gaussian mixture model to be processed and the corresponding model processing index data are obtained; wherein the model processing index data includes: target component values.
[0061] For example, the aforementioned Gaussian mixture model can be a Gaussian mixture model used in radar target tracking operations, or it can also be a Gaussian mixture model used in signal processing scenarios or sensor data fusion calculations. For example, a user can select the original Gaussian mixture model to be processed on a smart terminal device. For example, the user can currently select the Gaussian mixture model in the radar tracking target model as the original model to be processed on the terminal device. At the same time, the user can configure the corresponding target component value. This target component value can be the number of Gaussian components expected to be achieved after the model is simplified.
[0062] Exemplarily, the method further includes: configuring the model processing indicator data according to the corresponding task processing type and application scenario.
[0063] Specifically, users can customize model processing metrics when selecting a Gaussian mixture model to process. Alternatively, they can dynamically configure model processing metrics based on the number of Gaussian components in the model's initial state, the actual needs of the current business, or changes in the type of data the model is currently processing.
[0064] For example, the Gaussian components of the original Gaussian Mixture (GM) model in the radar target tracking model are M=10 to M=40, and the target component value of the current configuration is 5, that is, N=5.
[0065] In step S12, a greedy merging method is used to merge the Gaussian components in the original Gaussian mixture model until the number of Gaussian components reaches a target component value, so as to obtain an initial simplified model.
[0066] Exemplarily, the above step S12 may specifically include:
[0067] Step S121, merging any two Gaussian components in the original Gaussian mixture model to obtain multiple pairing solutions;
[0068] Step S122 , traverse each pairing scheme to select the optimal pairing scheme to merge the Gaussian components, and iterate until the number of Gaussian components reaches the target component value; wherein, in the optimal pairing scheme, the 2-Wasserstein distance between the Gaussian mixture model after the Gaussian components are merged and the original Gaussian mixture model is minimized.
[0069] Exemplarily, the method further includes: calculating the 2-Wasserstein distance between the two Gaussian mixture models based on the square of the 2-Wasserstein distance between the Gaussian components of the two Gaussian mixture models and the joint probability density distribution transmitted between the Gaussian components of the models.
[0070] Specifically, the formulas corresponding to the two GM models include:
[0071] F=α 1 f 1 +α 2 f 2 +…+α N1 f N1
[0072] G=β 1 g 1 +β 2 g 2 +…+β N2 g N2
[0073] Among them, f i (i=1,2…N1), g j (j=1, 2...N2) represent Gaussian distribution respectively.
[0074]
[0075] The Wasserstein distance metric between GM models is optimized based on discrete optimal transmission theory so that it can analytically express the distance between two GMs. The formula for defining the composite 2-Wasserstein distance includes:
[0076]
[0077] in, is the Gaussian component f i and g j The square of the 2-Wasserstein distance between 1 , α 2 , ...α N1 ) and β=(β 1 , β 2 , ...β N2), that is, α=(α 1 , α 2 , ...α N1 ) and β=(β 1 , β 2 1, ...β N2 ) is the set of all possible joint distributions that can be combined. * (i, j) exists and is unique.
[0078] Specifically, the original GM model is defined as f M . The original GM model f M Any two Gaussian components in Perform the merging process to obtain one component while keeping the other Gaussian components unchanged; the corresponding formulas include:
[0079]
[0080] w k is the weight after merging Gaussian components, μ k is the mean of the Gaussian distribution after merging the Gaussian components, ∑ k is the covariance of the Gaussian distribution after merging the Gaussian components.
[0081] The corresponding Gaussian component pairing scheme is denoted as π ij , traverse all the pairing schemes π of Gaussian components, select the optimal pairing scheme π, and satisfy the following conditions:
[0082] Note: f M-1 .
[0083] Based on the above method, iterate and traverse the combination pairing scheme of all Gaussian components until the original GM model has the required number of components N, which is recorded as f N , as the initial parsimonious model.
[0084] In step S13, the initial parsimonious model is weight-optimized based on the optimal transfer theory, so that the weight-optimized initial parsimonious model approaches the original Gaussian mixture model in terms of the composite 2-Wasserstein distance.
[0085] Exemplarily, weight optimization processing is performed on the initial parsimonious model based on the optimal transmission theory, including:
[0086] Step S131, defining a transmission cost matrix; wherein each element in the transmission cost matrix represents the square of the 2-Wasserstein distance between the Gaussian component of the original Gaussian mixture model and the Gaussian component in the initial simplified model;
[0087] Step S132, defining an optimization problem based on the 2-Wasserstein distance between the original Gaussian mixture model and the initial simplified model;
[0088] Step S133 , configuring constraint conditions based on the transmission amount between the Gaussian components of the model, and solving the optimization problem to obtain a weight optimization result corresponding to the initial simplified model.
[0089] Specifically, the original Gaussian mixture model f M The corresponding initial simplified GM model f N , optimize the weights of the initial minimalist GM model; its goal is to find a set of weights so that the minimalist GM model f N Best approximation of the original GM model f on the composite 2-Wasserstein distance M The corresponding formula can be expressed as:
[0090]
[0091] f M The Gaussian component weights and the probability density function of the Gaussian components, f N The Gaussian component weights and the probability density function of the Gaussian components.
[0092] Then, we can construct the cost matrix. Specifically, we define the transmission cost matrix Among them, each element It represents the square of the 2-Wasserstein distance between the i-th component in the original GM model and the j-th component in the initial parsimonious model, and the formula is expressed as:
[0093]
[0094] Then, the optimal transmission problem can be solved. Specifically, the marginal distribution is defined as the weight of the original GM model and the weights of the initial parsimonious GM model The transmission plan matrix γ = [γ(i, j)] is w 0 and w 1 The joint probability distribution of To simple portion The "transportation volume". According to the relationship between marginal probability distribution and joint probability distribution, we can get:
[0095]
[0096] Establish the optimization problem, expressed as:
[0097]
[0098] Substituting the formula into the equation, we get:
[0099]
[0100] The corresponding configurable constraints include:
[0101]
[0102] By solving equations (8) and (9) through linear programming, we can obtain the transmission plan matrix γ = [γ(i, j)], and then the weight of (4) can be obtained from (6).
[0103] In step S14, the K-Means clustering method is used to perform global optimization processing on the initial minimalist model after weight optimization, and the cluster center of the initial minimalist model is updated to meet the preset clustering iteration conditions to obtain a minimalist mixed Gaussian model.
[0104] Exemplarily, the above step S14 may specifically include:
[0105] Step S141, configuring the N Gaussian components of the initial parsimonious model after weight optimization as cluster centers;
[0106] Step S142, clustering the M Gaussian components of the original Gaussian mixture model based on the N cluster centers;
[0107] Step S143 : updating the cluster centers based on the distribution results of the Gaussian components until a preset clustering iteration condition is satisfied to obtain a simplified Gaussian mixture model.
[0108] Exemplarily, clustering the M Gaussian components of the original Gaussian mixture model based on N cluster centers includes:
[0109] Calculate the composite 2-Wasserstein distance between each Gaussian component of the original Gaussian mixture model and each cluster center;
[0110] Based on the distance calculation results, the Gaussian components are assigned to the cluster corresponding to the nearest cluster center; wherein each cluster center of the initial parsimonious model is configured with a corresponding cluster.
[0111] Exemplarily, updating the cluster center based on the distribution result of the Gaussian component includes:
[0112] The parameters of the cluster center are updated using the center of gravity formula corresponding to the 2-Wasserstein distance to achieve the update of the cluster center; the formula includes:
[0113]
[0114] Among them, wk is the weight after merging Gaussian components, μ k is the mean of the Gaussian distribution after merging the Gaussian components, ∑ k is the covariance of the Gaussian distribution after merging the Gaussian components.
[0115] Specifically, we can first calculate the initial cluster center, and for the initial parsimonious model f N , let the N components of the simplified GM model be cluster centers C = {c1, c2, ...c N}, each cluster center c k The corresponding cluster is C k .
[0116] Then, assign the Gaussian components to the nearest cluster center. Specifically, for the original GM model f M The M components s i ∈S, i∈{1, 2, ..., M}, assign it to the nearest cluster center c k The corresponding cluster C k , k∈{1, 2, ..., N}. That is, for each i∈{1, 2, ..., M}, if a Gaussian component s i To cluster center c k The distance to any other cluster center c t The distances between s and i Assigned to cluster C k ; The formula can be expressed as:
[0117]
[0118] Among them, d(s i , c k ) represents the component s i To center c k The corresponding formula can be expressed as:
[0119]
[0120] In order to conveniently express the relationship between components and cluster centers, the indicator function is expressed as:
[0121]
[0122] Then, the cluster center can be updated. Specifically, after determining the distribution results of each Gaussian component, the center of each cluster can be updated. Specifically, for each cluster, the parameters for calculating the cluster center can be updated using the following centroid formula corresponding to the 2-Wasserstein distance, which can be expressed as:
[0123]
[0124] Among them, w k is the weight after merging Gaussian components, μ k is the mean of the Gaussian distribution after merging the Gaussian components, and ∑k is the covariance of the Gaussian distribution after merging the Gaussian components.
[0125] Repeat the above steps until the position of the cluster center no longer changes significantly or the preset number of iterations is reached, and a simplified Gaussian mixture model is obtained.
[0126] Exemplarily, the model processing index data includes: model optimization index data defined based on the composite 2-Wasserstein distance. The method further includes:
[0127] Step S21, calculating the model distance between the simplified Gaussian mixture model and the original Gaussian mixture model based on the composite 2-Wasserstein distance;
[0128] Step S22: Compare the model distance with the model optimization index data to obtain a model simplicity evaluation result.
[0129] Specifically, users can pre-configure Gaussian model optimization metrics, such as the model distance defined by the composite 2-Wasserstein distance. For example, after completing model reduction and obtaining a reduced Gaussian mixture model, a reduced model evaluation task can be created, where the composite 2-Wasserstein distance can be used to measure the distance between the original GM model and the reduced GM model. If this distance is less than a preset distance threshold, the smaller the metric, the closer the reduced model is to the original model, and the better the performance of the reduced model. This allows for accurate evaluation of Gaussian mixture models.
[0130] In some exemplary embodiments, simulation data can be constructed to verify the present method. First, simulation data can be generated, and the parameters of the GM model are set: the covariance is generated using the Wishart distribution. For the d-dimensional Wishart distribution W d (d+5,0.01I d ), the weights and means can be randomly drawn from the following ranges:
[0131] w i ∈[0.02, 0.5]
[0132] μ i ∈[0, 3]
[0133] The data generated by d=2 and d=4 are used for the experiment. The original GM model with Gaussian components ranging from M=10 to M=40 is considered and simplified to a GM (N=5) model with only 5 components.
[0134] refer to Figure 3 、 Figure 4 As shown, compared with the existing COWA, West, GMRC, and Runnalls methods, the simplified GM model of the present invention is closer to the original GM model in terms of composite 2-Wasserstein distance, that is, the performance is better.
[0135] The method provided in the embodiment of the present invention constructs a three-stage optimization framework by introducing a resolvable composite 2-Wasserstein distance as a similarity measure between GMs. Specifically, refer to Figure 2 As shown, a greedy merging strategy is first used to iteratively merge adjacent Gaussian components to quickly compress the model size. Subsequently, based on optimal transmission theory, weights are dynamically adjusted to bring the simplified model closer to the original model in terms of probability distribution. Finally, an improved global K-means clustering optimization eliminates the risk of local optimality, further enhancing the ability to retain key information such as multimodality and tail features. This method effectively reduces computational costs while preserving the key structural features of the original model. It overcomes the inherent limitations of traditional KLD-based methods, such as the difficulty in accurately measuring structural differences when Gaussian components are close, KLD asymmetry, and the unsolvable KLD calculation between GMs. This provides a more accurate and stable GM simplification solution for radar target tracking, signal processing, sensor data fusion, and other fields, and can be extended to other hybrid model optimization tasks.
[0136] It should be noted that the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention and are not intended to be limiting. It is readily understood that the processes illustrated in the above figures do not indicate or limit the temporal order of these processes. Furthermore, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.
[0137] It should be noted that, although several modules or units of the device for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to an embodiment of the present invention, the features and functions of two or more modules or units described above can be concretized in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided into multiple modules or units to be concretized.
[0138] Figure 5 A schematic diagram of an electronic device suitable for implementing an embodiment of the present invention is shown.
[0139] It should be noted that Figure 5 The electronic device 1000 shown is only an example and should not limit the functions and scope of use of the embodiments of the present invention.
[0140] like Figure 5 As shown, electronic device 1000 includes a central processing unit (CPU) 1001, which can perform various appropriate actions and processes according to the program stored in read-only memory (ROM) 1002 or the program loaded from storage portion 1008 into random access memory (RAM) 1003. Various programs and data required for system operation are also stored in RAM 1003. CPU 1001, ROM 1002 and RAM 1003 are connected to each other via bus 1004. Input / output (I / O) interface 1005 is also connected to bus 1004.
[0141] The following components are connected to the I / O interface 1005: an input section 1006 including a keyboard, a mouse, and the like; an output section 1007 including devices such as a cathode ray tube (CRT), a liquid crystal display (LCD), and a speaker; a storage section 1008 including a hard disk and the like; and a communication section 1009 including a network interface card such as a LAN (Local Area Network) card or a modem. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to the I / O interface 1005 as needed. Removable media 1011, such as a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory, is installed in the drive 1010 as needed, so that computer programs read therefrom can be installed into the storage section 1008 as needed.
[0142] In particular, according to an embodiment of the present invention, the process described below with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present invention includes a computer program product that includes a computer program carried on a storage medium, the computer program containing program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network via the communication section 1009 and / or installed from a removable medium 1011. When the computer program is executed by the central processing unit (CPU) 1001, the various functions defined in the system of the present application are performed.
[0143] It should be noted that the storage medium shown in the embodiments of the present invention can be a computer-readable signal medium or a computer-readable storage medium or any combination of the above. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or component, or any combination of the above. More specific examples of computer-readable storage media can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash memory, an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, device or device. In the present invention, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any storage medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code contained on the storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, or any suitable combination thereof.
[0144] The flowcharts and block diagrams in the accompanying drawings illustrate the possible implementation architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present invention. In this regard, each box in the flowchart or block diagram can represent a module, program segment, or a part of code, and the above-mentioned module, program segment, or a part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram or flowchart, and the combination of boxes in the block diagram or flowchart, can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.
[0145] The units involved in the embodiments of the present invention may be implemented in software or hardware, and the units described may also be provided in a processor. In some cases, the names of these units do not limit the units themselves.
[0146] It should be noted that, as another aspect, the present application also provides a storage medium, which can be included in an electronic device; or it can exist independently without being installed in the electronic device. The above storage medium carries one or more programs, and when the above one or more programs are executed by an electronic device, the electronic device implements the method described in the following embodiments. For example, the electronic device can implement the following Figure 1 The individual steps of the method are shown.
[0147] In one embodiment, the present application provides a computer program product, including a computer program, which implements the steps in the above-mentioned method embodiments when executed by a processor.
[0148] Furthermore, the above-described figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention and are not intended to be limiting. It is readily understood that the processes illustrated in the above-described figures do not indicate or limit the temporal order of these processes. Furthermore, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.
[0149] Other embodiments of the present invention will readily occur to those skilled in the art after considering the specification and practicing the invention herein. This application is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the invention being indicated by the claims.
[0150] It should be understood that the present invention is not limited to the exact construction described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof, which is limited only by the appended claims.
Claims
1. A simplified method for Gaussian mixture models based on composite 2-Wasserstein distance, characterized in that: The method comprises: Obtaining the original Gaussian mixture model to be processed and the corresponding model processing index data; wherein the model processing index data includes: target component value; Using a greedy merging method, the Gaussian components in the original Gaussian mixture model are merged until the number of Gaussian components reaches a target component value, so as to obtain an initial simplified model; The initial parsimonious model is weighted optimized based on the optimal transfer theory, so that the weight-optimized initial parsimonious model approaches the original Gaussian mixture model in terms of the composite 2-Wasserstein distance. The K-Means clustering method is used to perform global optimization on the initial minimalist model after weight optimization, and the cluster centers of the initial minimalist model are updated to meet the preset clustering iteration conditions to obtain a minimalist mixed Gaussian model.
2. The method according to claim 1, characterized in that Using a greedy merging method, the Gaussian components in the original Gaussian mixture model are merged until the number of Gaussian components reaches a target component value to obtain an initial simplified model, including: Merge any two Gaussian components in the original Gaussian mixture model to obtain multiple pairing solutions; Traverse each pairing scheme to select the optimal pairing scheme to merge the Gaussian components, and iterate until the number of Gaussian components reaches the target component value; among them, in the optimal pairing scheme, the 2-Wasserstein distance between the Gaussian mixture model after the Gaussian components are merged and the original Gaussian mixture model is the smallest.
3. The method according to claim 1 or 2, characterized in that The method further includes calculating the 2-Wasserstein distance between the two Gaussian mixture models based on the square of the 2-Wasserstein distance between the Gaussian components of the two Gaussian mixture models and the joint probability density distribution of transmission between the Gaussian components of the models.
4. The method according to claim 1, wherein The initial parsimonious model is weighted and optimized based on the optimal transmission theory, including: Define a transmission cost matrix; where each element in the transmission cost matrix represents the square of the 2-Wasserstein distance between the Gaussian component of the original Gaussian mixture model and the Gaussian component in the initial simplified model; The optimization problem is defined based on the 2-Wasserstein distance between the original Gaussian mixture model and the initial parsimonious model; Based on the transmission amount between the Gaussian components of the model, the constraints are configured and the optimization problem is solved to obtain the weight optimization result corresponding to the initial simple model.
5. The method according to claim 1, wherein The K-Means clustering method is used to perform global optimization on the initial minimalist model after weight optimization, and the cluster centers of the initial minimalist model are updated to meet the preset clustering iteration conditions to obtain a minimalist mixed Gaussian model, including: The N Gaussian components of the initial parsimonious model after weight optimization are configured as cluster centers; Clustering is performed on the M Gaussian components of the original Gaussian mixture model based on N cluster centers; The cluster centers are updated based on the distribution results of the Gaussian components until the preset clustering iteration conditions are met to obtain a simplified mixed Gaussian model.
6. The method according to claim 5, characterized in that Clustering is performed on the M Gaussian components of the original Gaussian mixture model based on N cluster centers, including: Calculate the composite 2-Wasserstein distance between each Gaussian component of the original Gaussian mixture model and each cluster center; Based on the distance calculation results, the Gaussian components are assigned to the cluster corresponding to the nearest cluster center; wherein each cluster center of the initial parsimonious model is configured with a corresponding cluster.
7. The method according to claim 5, characterized in that The cluster center is updated based on the distribution results of the Gaussian components, including: The parameters of the cluster center are updated using the center of gravity formula corresponding to the 2-Wasserstein distance to achieve the update of the cluster center; the formula includes: Among them, w k is the weight after merging Gaussian components, μ k is the mean of the Gaussian distribution after merging the Gaussian components, ∑ k is the covariance of the Gaussian distribution after merging the Gaussian components.
8. The method according to claim 1, characterized in that The model processing index data includes: model optimization index data defined based on the composite 2-Wasserstein distance; The method further comprises: Calculating a model distance between the reduced Gaussian mixture model and the original Gaussian mixture model based on a composite 2-Wasserstein distance; The model distance is compared with the model optimization index data to obtain a model simplicity evaluation result.
9. The method according to claim 1, characterized in that The method further comprises: The model processing indicator data is configured according to the corresponding task processing type and application scenario.
10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the Gaussian mixture model reduction method based on composite 2-Wasserstein distance according to any one of claims 1 to 9 is implemented.