CN109670537A - The full attribute weight fuzzy clustering method of multicore based on quasi- Monte Carlo feature - Google Patents
The full attribute weight fuzzy clustering method of multicore based on quasi- Monte Carlo feature Download PDFInfo
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- CN109670537A CN109670537A CN201811464334.9A CN201811464334A CN109670537A CN 109670537 A CN109670537 A CN 109670537A CN 201811464334 A CN201811464334 A CN 201811464334A CN 109670537 A CN109670537 A CN 109670537A
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- G06F18/23—Clustering techniques
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- G06F18/00—Pattern recognition
- G06F18/20—Analysing
- G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
- G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
Abstract
A kind of full attribute weight fuzzy clustering method of multicore based on quasi- Monte Carlo feature, it is accurate approximate due to using quasi- Monte Carlo feature to carry out kernel function, and it is clustered in feature space, time complexity is very low, it can be used for handling large-scale data, by using multiple kernel functions, solve the problems, such as that kernel function is difficult to choose in advance.By using maximum-entropy technique, a weight is assigned for each characteristic dimension, so that important core and important dimension is played bigger effect in cluster, achieves the accuracy rate of existing Clustering Algorithm of Kernel above all.
Description
Technical field
The present invention relates to Clustering Algorithm of Kernel technical fields, and in particular to a kind of multicore based on quasi- Monte Carlo feature belongs to entirely
Property weighted fuzzy clustering method.
Background technique
Clustering Algorithm of Kernel is a kind of unsupervised machine learning method, is data mining, pattern-recognition and statistical analysis
Effective means.Initial data is mapped in nuclear space, is then existed according to data by kernel function by traditional Clustering Algorithm of Kernel
Similitude in nuclear space realizes data classification, can effectively find the number of other, non-spherical shapes hidden in data.However traditional core
The time complexity of clustering algorithm is very high, it is difficult to practical application.How Clustering Algorithm of Kernel in practical applications available is improved
Property become a research hotspot.
Traditional Clustering Algorithm of Kernel:
Clustering Algorithm of Kernel can be divided into two classes: monokaryon clustering algorithm and multicore clustering algorithm.In addition to the above-mentioned high time is complicated
Outside the shortcomings that spending, there is also other deficiencies for both methods.Monokaryon clustering algorithm needs selected kernel function in advance and kernel function ginseng
Number, but in practical application, suitable kernel function type and nuclear parameter value can not be learnt in advance, in this case, monokaryon is poly-
Class algorithm is difficult to obtain ideal result；Multicore clustering algorithm is set by using multiple kernel functions or for the same kernel function
Multiple and different nuclear parameters solves the problems, such as that kernel function, nuclear parameter are difficult to choose in advance to a certain extent, but multicore is poly-
The cluster accuracy rate of class algorithm is often unsatisfactory.
Quasi- Monte Carlo feature:
Quasi- Monte Carlo is characterized in a kind of random character method that constant kernel function is moved for approximately linear, by original number
According to being mapped in low order feature space.In this feature space, the inner product of two features is approximately equal to kernel function.Compared to other
Random character method, quasi- Monte Carlo feature are more acurrate to the approximation of kernel function.Current quasi- Monte Carlo feature is only used for list
In Clustering Algorithm of Kernel, it can not effectively solve the problems, such as that kernel function and nuclear parameter are difficult to choose.
Summary of the invention
That to overcome the above deficiencies, the invention provides a kind of time complexities is extremely low, kernel function choose it is simple,
Accuracy rate is higher than the full attribute weight fuzzy clustering method of the multicore based on quasi- Monte Carlo feature of all existing kernel clustering methods.
The present invention overcomes the technical solution used by its technical problem to be:
A kind of full attribute weight fuzzy clustering method of multicore based on quasi- Monte Carlo feature, includes the following steps:
A) computer reads in data set X={ x to be clusteredn| 1≤n≤N }, wherein xnIndicate nth data, N is by counting
The data amount check that calculation machine obtains data set pxrd analysis；
B) user chooses L kernel function k1,k2,...,kL, L is the number of the kernel function of user's input；
C) computer is calculated and first of kernel function k using quasi- Monte Carlo characteristics algorithmlCorresponding Feature Mapping function Ψl
(), wherein 1≤l≤L, the characteristic dimension M in quasi- Monte Carlo characteristics algorithm is set as 200；D uses first of Feature Mapping letter
Number ΨlInput data x is calculated in ()nLow order random character Ψl(xn), wherein 1≤l≤L, 1≤n≤N, all by first of spy
Levy mapping function ΨlThe low order random character Ψ that () is calculatedl(xn) composition aggregated label be first of feature space Sl,
In 1≤l≤L；
E) computer is random to low order using the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature
Feature Ψl(xn) cluster calculation is carried out, wherein 1≤l≤L, 1≤n≤N；
F) computer is random to low order according to the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature
Feature Ψl(xn) clustered to obtain degree of membership and obtain data set X={ xn| 1≤n≤N } classification results.Further, step
E) the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature in includes the following steps:
E-1) the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature is initialized, is used
Family inputs the class centric quantity K in algorithm, and user inputs the coefficient gamma in algorithm, 0.001≤γ≤0.1, by the mould in algorithm
Paste factor alpha is set as 2.0, sets 0.000001 for the stopping threshold values ξ in algorithm, the iteration count t=in algorithm is arranged
0, the initial value of algorithm objective function is set as J(o)=-9999；
E-2) computer is from first of feature space SlIn randomly select a low order random character, as first spy
Levy the class center c of kth class in spacekl, wherein 1≤k≤K, 1≤l≤L, are realized complete to the multicore based on quasi- Monte Carlo feature
The class center of every one kind is initialized in each feature space in attribute weight fuzzy clustering algorithm；
E-3 willWeight w as the m dimension of kth class in first of feature spaceklm, wherein 1≤l≤L, 1≤k
≤ K, 1≤m≤M are realized empty to feature each in the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature
Between in the weight of every each dimension of one kind initialized.
E-4 iteration count) is made to add 1, i.e. t+1；
E-5) computer passes through formula
Calculate data xnBelong to k-th of class
Degree of membership unk, wherein 1≤n≤N, 1≤k≤K, Ψlm(xn) it is input data xnLow order in first of feature space is special at random
Levy Ψl(xn) m dimension, 1≤l≤L, 1≤m≤M, 1≤n≤N；cklmIt is the class center c of kth class in first of feature spacekl
M dimension, 1≤k≤K, 1≤l≤L, 1≤m≤M；whlmBe h class in first of feature space m dimension weight, 1≤h≤
K, 1≤l≤L, 1≤m≤M；chlmIt is the class center c of h class in first of feature spacehlM dimension, 1≤h≤K, 1≤l≤L,
1≤m≤M；
E-6) computer passes through formula
Calculate the class center c for updating kth class in first of feature spaceklM
Dimension, wherein 1≤l≤L, 1≤m≤M, 1≤n≤N；
E-7) pass through formula
It updates in first of feature space
The weight of the m dimension of kth class, 1≤k≤K, 1≤l≤L, 1≤m≤M, Ψrs(xn) it is input data xnIn r-th of feature space
In low order random character Ψr(xn) s dimension, 1≤r≤L, 1≤s≤M, 1≤n≤N, ckrsIt is kth in r-th of feature space
The class center c of classkrS dimension, 1≤k≤K, 1≤r≤L, 1≤s≤M；
E-8) pass through formula
Calculate the objective function J that the t times iteration obtains(t)；
E-9) computer calculates complete the t times iteration of attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature
Obtained objective function J(t)With the objective function J of the t-1 times iteration(t-1)Between difference, such as | | J(t)-J(t-1)| | >=ξ is held
Row e-3), such as | | J(t)-J(t-1)| | < ξ is executed f).
The beneficial effects of the present invention are: it is accurate approximate due to using quasi- Monte Carlo feature to carry out kernel function, and in spy
Sign space is clustered, and time complexity is very low, can be used for handling large-scale data, by using multiple kernel functions, is effectively solved
Kernel function of having determined is difficult to the problem of choosing in advance.By using maximum-entropy technique, a weight is assigned for each characteristic dimension,
So that important core and important dimension is played bigger effect in cluster, achieves the standard of existing Clustering Algorithm of Kernel above all
True rate.
Specific embodiment
The present invention will be further described below.
A kind of full attribute weight fuzzy clustering method of multicore based on quasi- Monte Carlo feature, includes the following steps:
A) computer reads in data set X={ x to be clusteredn| 1≤n≤N }, wherein xnIndicate nth data, N is by counting
The data amount check that calculation machine obtains data set pxrd analysis；
B) user chooses L kernel function k1,k2,...,kL, L is the number of the kernel function of user's input；
C) computer is calculated and first of kernel function k using quasi- Monte Carlo characteristics algorithmlCorresponding Feature Mapping function Ψl
(), wherein 1≤l≤L, the characteristic dimension M in quasi- Monte Carlo characteristics algorithm is set as 200；D uses first of Feature Mapping letter
Number ΨlInput data x is calculated in ()nLow order random character Ψl(xn), wherein 1≤l≤L, 1≤n≤N, all by first of spy
Levy mapping function ΨlThe low order random character Ψ that () is calculatedl(xn) composition aggregated label be first of feature space Sl,
In 1≤l≤L；
E) computer is random to low order using the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature
Feature Ψl(xn) cluster calculation is carried out, wherein 1≤l≤L, 1≤n≤N；
F) computer is random to low order according to the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature
Feature Ψl(xn) clustered to obtain degree of membership and obtain data set X={ xn| 1≤n≤N } classification results.Due to using quasi- illiteracy
Special Carlow feature carries out accurate approximation to kernel function, and is clustered in feature space, and time complexity is very low, can be used for handling
Large-scale data solves the problems, such as that kernel function is difficult to choose in advance by using multiple kernel functions.By using maximum
Entropy technique assigns a weight for each characteristic dimension, plays important core and important dimension in cluster bigger
Effect, achieves the accuracy rate of existing Clustering Algorithm of Kernel above all.
Embodiment 1:
The full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature in step e) includes the following steps:
E-1) the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature is initialized, is used
Family inputs the class centric quantity K in algorithm, and user inputs the coefficient gamma in algorithm, 0.001≤γ≤0.1, by the mould in algorithm
Paste factor alpha is set as 2.0, sets 0.000001 for the stopping threshold values ξ in algorithm, the iteration count t=in algorithm is arranged
0, the initial value of algorithm objective function is set as J(o)=-9999；
E-2) computer is from first of feature space SlIn randomly select a low order random character, as first spy
Levy the class center c of kth class in spacekl, wherein 1≤k≤K, 1≤l≤L, are realized complete to the multicore based on quasi- Monte Carlo feature
The class center of every one kind is initialized in each feature space in attribute weight fuzzy clustering algorithm；
E-3 willWeight w as the m dimension of kth class in first of feature spaceklm, wherein 1≤l≤L, 1≤k
≤ K, 1≤m≤M are realized empty to feature each in the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature
Between in the weight of every each dimension of one kind initialized.
E-4 iteration count) is made to add 1, i.e. t+1；
E-5) computer passes through formula
Calculate data xnBelong to k-th of class
Degree of membership unk, wherein 1≤n≤N, 1≤k≤K, Ψlm(xn) it is input data xnLow order in first of feature space is special at random
Levy Ψl(xn) m dimension, 1≤l≤L, 1≤m≤M, 1≤n≤N；cklmIt is the class center c of kth class in first of feature spacekl
M dimension, 1≤k≤K, 1≤l≤L, 1≤m≤M；whlmBe h class in first of feature space m dimension weight, 1≤h≤
K, 1≤l≤L, 1≤m≤M；chlmIt is the class center c of h class in first of feature spacehlM dimension, 1≤h≤K, 1≤l≤L,
1≤m≤M；
E-6) computer passes through formula
Calculate the class center c for updating kth class in first of feature spaceklM
Dimension, wherein 1≤l≤L, 1≤m≤M, 1≤n≤N；
E-7) pass through formula
It updates in first of feature space
The weight of the m dimension of kth class, 1≤k≤K, 1≤l≤L, 1≤m≤M, Ψrs(xn) it is input data xnIn r-th of feature space
In low order random character Ψr(xn) s dimension, 1≤r≤L, 1≤s≤M, 1≤n≤N, ckrsIt is kth in r-th of feature space
The class center c of classkrS dimension, 1≤k≤K, 1≤r≤L, 1≤s≤M；
E-8) pass through formula
Calculate the objective function J that the t times iteration obtains(t)；
E-9) computer calculates complete the t times iteration of attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature
Obtained objective function J(t)With the objective function J of the t-1 times iteration(t-1)Between difference, such as | | J(t)-J(t-1)| | >=ξ is held
Row e-3), such as | | J(t)-J(t-1)| | < ξ is executed f).
Claims (2)
1. a kind of full attribute weight fuzzy clustering method of multicore based on quasi- Monte Carlo feature, which is characterized in that including as follows
Step:
A) computer reads in data set X={ x to be clusteredn| 1≤n≤N }, wherein xnIndicate nth data, N is by computer
The data amount check that data set pxrd analysis is obtained；
B) user chooses L kernel function k1,k2,...,kL, L is the number of the kernel function of user's input；
C) computer is calculated and first of kernel function k using quasi- Monte Carlo characteristics algorithmlCorresponding Feature Mapping function Ψl(),
Wherein 1≤l≤L, the characteristic dimension M in quasi- Monte Carlo characteristics algorithm are set as 200；D uses first of Feature Mapping function
ΨlInput data x is calculated in ()nLow order random character Ψl(xn), wherein 1≤l≤L, 1≤n≤N, all by first of feature
Mapping function ΨlThe low order random character Ψ that () is calculatedl(xn) composition aggregated label be first of feature space Sl, wherein
1≤l≤L；
E) computer is using the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature to low order random character
Ψl(xn) cluster calculation is carried out, wherein 1≤l≤L, 1≤n≤N；
F) computer is according to the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature to low order random character
Ψl(xn) clustered to obtain degree of membership and obtain data set X={ xn| 1≤n≤N } classification results.
2. the full attribute weight fuzzy clustering method of the multicore according to claim 1 based on quasi- Monte Carlo feature, special
Sign is: the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature in step e) includes the following steps:
E-1) the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature is initialized, user is defeated
Enter the class centric quantity K in algorithm, user inputs the coefficient gamma in algorithm, 0.001≤γ≤0.1, by the fuzzy system in algorithm
Number α is set as 2.0, sets 0.000001 for the stopping threshold values ξ in algorithm, the iteration count t=0 in algorithm is arranged, calculate
The initial value of method objective function is set as J(o)=-9999；
E-2) computer is from first of feature space SlIn randomly select a low order random character, it is empty as first feature
Between middle kth class class center ckl, wherein 1≤k≤K, 1≤l≤L, are realized to the full attribute of multicore based on quasi- Monte Carlo feature
The class center of every one kind is initialized in each feature space in weighted fuzzy clustering algorithm；
E-3 willWeight w as the m dimension of kth class in first of feature spaceklm, wherein 1≤l≤L, 1≤k≤K, 1
≤ m≤M is realized to every in each feature space in the full attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature
It is a kind of to be initialized per one-dimensional weight.
E-4 iteration count) is made to add 1, i.e. t+1；
E-5) computer passes through formula
Calculate data xnBelong to being subordinate to for k-th of class
Spend unk, wherein 1≤n≤N, 1≤k≤K, Ψlm(xn) it is input data xnLow order random character in first of feature space
Ψl(xn) m dimension, 1≤l≤L, 1≤m≤M, 1≤n≤N；cklmIt is the class center c of kth class in first of feature spacekl's
M dimension, 1≤k≤K, 1≤l≤L, 1≤m≤M；whlmBe h class in first of feature space m dimension weight, 1≤h≤K,
1≤l≤L, 1≤m≤M；chlmIt is the class center c of h class in first of feature spacehlM dimension, 1≤h≤K, 1≤l≤L, 1
≤m≤M；
E-6) computer passes through formula
Calculate the class center c for updating kth class in first of feature spaceklM dimension,
In 1≤l≤L, 1≤m≤M, 1≤n≤N；
E-7) pass through formula
Update kth in first of feature space
The weight of the m dimension of class, 1≤k≤K, 1≤l≤L, 1≤m≤M, Ψrs(xn) it is input data xnIn r-th of feature space
Low order random character Ψr(xn) S dimension, 1≤r≤L, 1≤s≤M, 1≤n≤N, ckrsIt is kth class in r-th of feature space
Class center ckrS dimension, 1≤k≤K, 1≤r≤L, 1≤s≤M；
E-8) pass through formula
Calculate the objective function J that the t times iteration obtains(t)；
E-9) computer calculates complete the t times iteration of attribute weight fuzzy clustering algorithm of multicore based on quasi- Monte Carlo feature and obtains
Objective function J(t)With the objective function J of the t-1 times iteration(t-1)Between difference, such as
||J(t)-J(t-)| | >=ξ executes e-3), such as | | J(t)-J(t-1)| | < ξ is executed f).
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