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Gaussian mixture model parameter estimation algorithm based on enhanced online search principle

A technology of mixed Gaussian model and parameter estimation algorithm, which is applied in the field of parameter estimation algorithm, parameter estimation problem in mixed Gaussian model, and parameter estimation algorithm field of mixed Gaussian model, which can solve problems such as non-optimal and numerical instability

Pending Publication Date: 2020-05-29
NANJING MEDICAL UNIV
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Problems solved by technology

The well-known Aitken acceleration process can be considered as an online search algorithm, which needs to calculate the inverse operation of the second-order partial derivative of the objective function, such as the Jacobian determinant, etc. However, this type of algorithm will encounter numerical instability
In order to solve this situation, an online search method (λ-EM) defines the search direction as the difference between two adjacent parameters, however, the calculation of the search step size of this algorithm is not optimal

Method used

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  • Gaussian mixture model parameter estimation algorithm based on enhanced online search principle
  • Gaussian mixture model parameter estimation algorithm based on enhanced online search principle
  • Gaussian mixture model parameter estimation algorithm based on enhanced online search principle

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Embodiment 1

[0083] In order to evaluate the robustness of the algorithm, 50 initialization points are used. For detailed initialization strategies, see figure 1 . The index package of the evaluation algorithm is the average estimation error e of each iteration (it) and the average maximum likelihood function It is defined as follows:

[0084]

[0085]

[0086] Among them, R=50, N() is a multidimensional Gaussian distribution, is the rth initialization parameter. π k In order to minimize the mapping relationship of one-to-one weight matching, is a symmetric Kullback divergence.

[0087] First, Table 1 gives the time complexity of different algorithms under each iteration condition.

[0088] In the following two cases (two components in equilibrium and non-equilibrium, K=2, GMM), first, the mean value of our simulation: μ 1 =[0,0] T ,μ 1 =[50,0] T . The covariance is: Σ 1 =Σ 2 =[100,0;0,100] T . The mixing coefficient can be given by the following formula, Table 1...

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Abstract

The invention discloses a Gaussian mixture model (GMM) parameter estimation algorithm based on an enhanced online search (ELS) principle, which is used for solving the problem of low convergence rateof a Gaussian mixture model and an expectation maximization algorithm (EM algorithm) in an unbalanced state, and comprises the following steps of: (1) importing a multi-dimensional sample set; (2) calculating an E-step by adopting an EM algorithm to obtain a posterior probability density function; (3) performing step length calculation in a given direction towards the direction of a final solutionaccording to an ELS principle; according to an initial target function, namely maximum likelihood estimation, easily calculating a required step length by rooting a second-order polynomial; and (4) judging the reasonability of the new step length, and updating parameters in the Gaussian mixture model, i.e., calculating the M-step. According to an enhanced online search principle, the convergencespeed and convergence precision of a traditional EM algorithm are increased.

Description

technical field [0001] The invention relates to a parameter estimation algorithm in the field of machine learning, in particular to a mixed Gaussian model parameter estimation algorithm based on the enhanced online search principle, which belongs to the parameter estimation problem in the mixed Gaussian model. Background technique [0002] The expectation maximization (EM) algorithm is one of the most popular algorithms in applied statistics, especially in the case of missing or hidden information, this algorithm can better optimize the maximum likelihood estimation problem. Gaussian mixture model (GMM) is a very useful data clustering tool, widely used in pattern recognition, data mining, image segmentation, feature selection and extraction, signal processing and other fields. GMM constructs the dataset samples as a linear mixed Gaussian distribution. The EM algorithm can effectively identify parameters in GMM, such as, under each category condition, mixing parameters, mea...

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Application Information

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IPC IPC(8): G06F17/18
CPCG06F17/18
Inventor 向文涛李建清徐争元刘宾朱松盛吴晓玲王伟
Owner NANJING MEDICAL UNIV
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