Method and device for determining statistical model parameter based on expectationmaximization algorithm
Method and device for determining statistical model parameter based on expectationmaximization algorithm
 CN 104,809,098 A
 Filed: 01/27/2014
 Published: 07/29/2015
 Est. Priority Date: 01/27/2014
 Status: Active Application
First Claim
1. determine a method for statistical model parameter, for the parameter based on N number of data point determination statistical model, wherein N be more than or equal to 2 integer, it is characterized in that, comprising:
 Receive comprise D attribute of N number of data point and N number of data point data set to be organized into input matrix, wherein D be more than or equal to 1 integer;
According to described input matrix, set K cluster centre, the initial value of described parameter and posterior probability matrix μ
_{n × K}(μ
_{n,k}) initial value wherein, posterior probability μ
_{n,k}represent the posterior probability of the nth data point on a kth cluster centre, wherein K be more than or equal to 2 integer, 1≤
n≤
N, 1≤
k≤
K, and according to and the calculation of initial value of described parameter Based on calculate the described parameter of the t time circulation, and calculate the residual error of described N number of data point at a described K cluster centre wherein t>
=1;
From described N number of data point, select M data point in the residual error of a described K cluster centre based on described N number of data point, and select L cluster centre from a described K cluster centre, wherein 1≤
M≤
N, 1≤
L≤
K;
The posterior probability of a described M data point on a described L cluster centre is calculated according to the described parameter that the t time cycle calculations obtains According to calculated described posterior probability upgrade the posterior probability matrix of described N number of data point on a described K cluster centre and based on the described posterior probability calculated upgrade the value of the described parameter of the t+1 time circulation;
Judge whether the described parameter circulated for the t+1 time restrains, when described parameter is for convergence, stop circulating and exporting described parameter.
Chinese PRB Reexamination
Abstract
The invention relates to a method and a device for determining a statistical model parameter based on an expectationmaximization algorithm, wherein the method comprises the following steps: setting K clustering centers, an initial value (a formula is provided) of a parameter and an initial value of a posterior probability matrix uNxK (un,k); and calculating (a formula is provided) based on (a formula is provided) and the initial value of the parameter; and calculating based on (a formula is provided) to obtain a parameter of the tth circulation; and calculating a residual error (a formula is provided) of N data points in the K clustering centers; selecting L clustering centers of M data points based on the residual error; calculating a posterior probability (a formula is provided) of the M data points in the L clustering centers based on the parameter obtained from the tth circulation of calculation; updating the posterior probability matrix (a formula is provided) of the N data points in the K clustering centers based on the calculated posterior probability (a formula is provided); and updating a value of a parameter of the (t+1)th circulation based on the calculated posterior probability (a formula is provided); judging whether the parameter of the (t+1)th circulation is converged; when the parameter is converged, stopping the circulation and outputting the parameter. The method and the device for determining the statistical model parameter based on the expectationmaximization algorithm can reduce the iteration cost and the time cost upon determining the parameter of the statistical model.

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10 Claims

1. determine a method for statistical model parameter, for the parameter based on N number of data point determination statistical model, wherein N be more than or equal to 2 integer, it is characterized in that, comprising:

Receive comprise D attribute of N number of data point and N number of data point data set to be organized into input matrix, wherein D be more than or equal to 1 integer; According to described input matrix, set K cluster centre, the initial value of described parameter and posterior probability matrix μ
_{n × K}(μ
_{n,k}) initial value wherein, posterior probability μ
_{n,k}represent the posterior probability of the nth data point on a kth cluster centre, wherein K be more than or equal to 2 integer, 1≤
n≤
N, 1≤
k≤
K, and according to and the calculation of initial value of described parameterBased on calculate the described parameter of the t time circulation, and calculate the residual error of described N number of data point at a described K cluster centre wherein t>
=1;
From described N number of data point, select M data point in the residual error of a described K cluster centre based on described N number of data point, and select L cluster centre from a described K cluster centre, wherein 1≤
M≤
N, 1≤
L≤
K;The posterior probability of a described M data point on a described L cluster centre is calculated according to the described parameter that the t time cycle calculations obtains According to calculated described posterior probability upgrade the posterior probability matrix of described N number of data point on a described K cluster centre and based on the described posterior probability calculated upgrade the value of the described parameter of the t+1 time circulation;
Judge whether the described parameter circulated for the t+1 time restrains, when described parameter is for convergence, stop circulating and exporting described parameter.


2. method according to claim 1, is characterized in that, describedly from described N number of data point, selects M data point in the residual error of a described K cluster centre based on described N number of data point, and selects L cluster centre from a described K cluster centre, comprising:

Calculate the residual error of each described data point and residual error r is selected from described N number of data point ^{t}_{n}m maximum data point;
According to the residual error of each data point at each described cluster centre for each data point in a described M data point, from a described K cluster centre, select residual error respectively l maximum cluster centre.


3. method according to claim 1, is characterized in that, describedly from described N number of data point, selects M data point in the residual error of a described K cluster centre based on described N number of data point, and selects L cluster centre from a described K cluster centre, comprising:

Calculate the residual error of each described data point and residual error is selected from a described K cluster centre l maximum cluster centre;
According to the residual error of each data point at each described cluster centre for each cluster centre of a described K cluster centre, from described N number of data point, select residual error respectively m maximum data point.


4. the method according to any one of claim 13, is characterized in that, the data set comprising D attribute of N number of data point and N number of data point in described reception, with after being organized into input matrix, also comprises:

Setting proportionality factors lambda _{n}and λ
_{k}, wherein 0<
λ
_{n}≤
0.5,0<
λ
_{k}≤
0.5;
According to described proportionality factors lambda _{n}and λ
_{k}calculate the value of described M and described L, wherein, M=λ
_{n}n, L=λ
_{k}k.


5. the method according to any one of claim 14, is characterized in that, judges whether the value of the described parameter circulated for the t+1 time restrains, and comprising:

Difference between the described parameter calculating the described parameter that obtains the t+1 time cycle calculations and obtain the t time cycle calculations; Judge whether the absolute value of described difference exceeds default threshold value; If the absolute value of all described differences is all less than described default threshold value, then determine the described parameter convergence of described the t+1 time circulation; If the absolute value of arbitrary described difference is not less than described default threshold value, then determine that the described parameter of described the t+1 time circulation does not restrain.


6. determine a device for statistical model parameter, for the parameter based on N number of data point determination statistical model, wherein N be more than or equal to 2 integer, it is characterized in that, comprising:

Load module, for receiving the data set of D the attribute comprising N number of data point and N number of data point to be organized into input matrix, wherein D be more than or equal to 1 integer; Initialization module, communicates with described load module, for according to described input matrix, sets K cluster centre, the initial value of described parameter and posterior probability matrix μ
_{n × K}(μ
_{n,k}) initial value wherein, posterior probability μ
_{n,k}represent the posterior probability of the nth data point on a kth cluster centre, wherein K be more than or equal to 2 integer, 1≤
n≤
N, 1≤
k≤
K, and according to and the calculation of initial value of described parameterResidual computations module, communicates with described initialization module, for based on calculate the described parameter of the t time circulation, and calculate the residual error of described N number of data point at a described K cluster centre ${r}_{n,k}^{t}={\mathrm{\μn,kt{\mathrm{mu;n,kt1,}}_{}^{}}}_{}^{}$ Wherein t >
=1;
Select module, communicate with described residual computations module, for selecting M data point in the residual error of a described K cluster centre based on described N number of data point from described N number of data point, and select L cluster centre from a described K cluster centre, wherein 1≤
M≤
N, 1≤
L≤
K;Posterior probability computing module, communicates with described selection module, calculates the posterior probability of a described M data point on a described L cluster centre for the described parameter obtained according to the t time cycle calculations Probability matrix update module, communicates with described posterior probability computing module and described residual computations module, for according to calculated described posterior probability upgrade the posterior probability matrix of described N number of data point on a described K cluster centre Parameter value calculation module, communicates with described probability matrix update module, for based on the described posterior probability calculated upgrade the value of the described parameter of the t+1 time circulation;
AndJudge module, communicates with described residual computations module and described parameter value calculation module, for judging whether the described parameter circulated for the t+1 time restrains, when described parameter is for convergence, stops circulating and exporting described parameter.


7. device according to claim 6, is characterized in that, described selection module is configured to:
 the residual error calculating each described data point and residual error r is selected from described N number of data point ^{t}_{n}m maximum data point;
According to the residual error of each data point at each described cluster centre for each data point in a described M data point, from a described K cluster centre, select residual error respectively l maximum cluster centre.
 the residual error calculating each described data point and residual error r is selected from described N number of data point ^{t}_{n}m maximum data point;

8. device according to claim 6, is characterized in that, described selection module is configured to:

Calculate the residual error of each described data point and residual error is selected from a described K cluster centre l maximum cluster centre;
According to the residual error of each data point at each described cluster centre for each cluster centre of a described K cluster centre, from described N number of data point, select residual error respectively m maximum data point.


9. the device according to any one of claim 68, is characterized in that, described initialization module is configured to, setting proportionality factors lambda _{n}and λ

_{k}, wherein 0<
λ
_{n}≤
0.5,0<
λ
_{k}≤
0.5;
According to described proportionality factors lambda _{n}and λ
_{k}calculate the value of described M and described L, wherein, M=λ
_{n}n, L=λ
_{k}k.

_{k}, wherein 0<

10. the device according to any one of claim 69, is characterized in that, described judge module is configured to:

Difference between the described parameter calculating the described parameter that obtains the t+1 time cycle calculations and obtain the t time cycle calculations; Judge whether the absolute value of described difference exceeds default threshold value; If the absolute value of all described differences is all less than described default threshold value, then determine the described parameter convergence of described the t+1 time circulation; If the absolute value of arbitrary described difference is not less than described default threshold value, then determine that the described parameter of described the t+1 time circulation does not restrain.

Specification(s)