CN106022359A - Fuzzy entropy space clustering analysis method based on orderly information entropy - Google Patents

Abstract

The invention discloses a fuzzy entropy space clustering analysis method based on orderly information entropy, comprising the following steps: S1, inputting a standardized matrix, and letting an integer i=1; S2, assigning an ith value corresponding to a relationship set D to a fuzzy entropy space parameter, and initializing intermediate sets A and C; S3, letting an intermediate set B be empty; S4, if R(xj, xk)>=lambda, deciding that B=B union {xj} and A=A\{xj}; S5, if R(xj, xk)>=lambda, deciding that B=B union {xs} and A=A\{xs}, or going to S6; S6, letting C=C union {B}, and letting an integer i+1 assign a value to i; repeating the steps S2 to S6 until the integer i is equal to the size m of the relationship set D; S7, if A is empty, deciding that X(lambda)=C, and calculating the orderly information entropy at the moment; S8, if HP(min)=min{X(lambda)}, deciding that min=lambda and going to S9, or going to S2; and S9, outputting an optimal granularity level.

Description

Fuzzy entropy space cluster analysis method based on ordered information entropy

Technical field

The present invention relates to cluster analysis field, particularly relate to a kind of fuzzy entropy space cluster analysis based on ordered information entropy Method.

Background technology

Cluster, as an ancient problem, along with generation and the development of human society deepen constantly.Cluster analysis is machine An important field of research in device learning areas.It is an important method of rule between research discrete data.Cluster All it is widely used in a lot of fields, the aspect such as including pattern recognition, data mining and marketing research.The target of cluster is On the premise of there is no any priori, data are gathered into different classes, find character the most essential between sample point, make Class inherited is big as far as possible, and in class, diversity is the least.People have carried out various different research to cluster very early, pass The clustering algorithm of system substantially can be divided into following a few class: division methods, hierarchical method, method based on density, based on grid Method and method based on model.By cluster analysis, we can from the interesting knowledge of extracting data, rule or other Information, it is possible to observe from different perspectives, the knowledge of discovery may be used for decision-making, process control, information management etc..Existing Technology mainly has partition clustering, hierarchical clustering, density clustering and cluster based on grid, but great majority are fuzzy Cluster is required for artificially specifying clusters number.Initial cluster center, to initializing sensitivity, it is difficult to obtain global optimum.And at present Clustering algorithm based on Fuzzy Quotient Spaces, draw is the cluster result of a hierarchical, but cannot know which grain Degree level is an optimal cluster result.

Summary of the invention

The goal of the invention of the present invention is, it is provided that the base of a kind of optimal level that can select under Fuzzy Quotient Spaces In the fuzzy entropy space cluster analysis method of ordered information entropy,.

The technical solution adopted for the present invention to solve the technical problems is:

The present invention provides a kind of fuzzy entropy space cluster analysis method based on ordered information entropy, comprises the following steps:

S1: input normalized matrix X={x₁, x₂, x₃..., x_n, R be a fuzzy equivalence relation on X or Similarity relation, then set of relationship D={R (x, y) | x, y ∈ X}={ λ₁, λ₂, λ₃..., λ_m, 1=λ₁＞ λ₂＞ λ₃＞ ... ＞ λ_m, wherein λ_i(i=1,2,3 ..., m) for fuzzy upper spatial parameter；Make integer i=1；

S2: i-th value corresponding for set of relationship D is assigned to fuzzy entropy spatial parameter λ, λ=λ_i, initialize middle set In the middle of A, and assignment, set A is and X an equal amount of positive integer collection, A={1,2,3 ..., n}；Set C in the middle of initializing, And assignment C is empty,

S3: in the middle of order, set B is empty,Take arbitrary integer j ∈ A, B=B ∪ { x_j, A=A { x_j}；

S4: take arbitrary integer k ∈ A, if R is (x_j, x_k) >=λ, then B=B ∪ { x_j, A=A { x_j}；Take arbitrary Integer s ∈ A, if R is (x_j, x_k) >=λ, then B=B ∪ { x_s, A=A { x_s, otherwise turn S5；

S5: make C=C ∪ { B}, and make integer i+1 be assigned to i；Repeated execution of steps S2～S5, until integer i is equal to closing Assembly closes size m of D, repeats to terminate；

S6: ifThen X (λ)={ x₁, x₂, x₃... x_k..., x_λ}=C,

Calculate ordered information entropy HP (X (λ)) now (k=1,2,3,4 ..., λ)；

S7: if HP (min)=min{X (λ) }, then min=λ, turn S8, otherwise turn S2；

S8: export optimal granularity level X (min)=C.

In method of the present invention, step 6 calculates X (λ)={ x₁, x₂, x₃... x_k..., x_λThe ordered information of }=C Entropy concretely comprises the following steps:

Phase space reconfiguration is used to postpone coordinate method to either element x in X (λ)_iCarry out phase space reconfiguration, to each sampled point Take m sampling point of its continuous print, obtain an x_iM-dimensional space reconstruct vector: x_i=x (i), x (i+1) ..., x (i+ (m- L) * l) },

Then the phase space matrix of sequence X is:When wherein m and l is respectively reconstruct dimension and postpones Between；

Reconstruct vector x to x (i)_iEach element carries out ascending order arrangement, obtains:

x_i={ x (i+ (j₁-1)*l)≤x(i+(j₂-1)*l)≤…≤i+(j_m-1)*l}

The arrangement mode obtained is { j₁, j₂, j₃..., j_m}

It is fully intermeshing m！In one, arranging situation occurrence numbers various to X sequence are added up, and calculate various arrangement The relative frequency that situation occurs is as its Probability p₁、p₂、…p_k, k≤m！, arrangement entropy after sequence of calculation normalization:

$H=(-{\mathrm{\Σ}}_{i=1}^k{p}_i*{\log }_2(p_i\left)\right)*{\log }_2(m!).$

The beneficial effect comprise that: the present invention utilizes the set of relationship under Fuzzy Quotient Spaces to replace traditional fuzzy C Euclidean distance in means clustering algorithm, utilizes criterion function ordered information entropy based on granularity thought to select one Good level, so that it is determined that the number of cluster, and select there is the high sample of similarity as initial cluster center.The present invention is also Introduce entropy computing, have amount of calculation compared with little, take the advantages such as computer storage unit is few, method is simple, it is adaptable to large sample Cluster analysis, and the method for the present invention need not pre-establish cluster numbers, it appeared that the hierarchical relationship of class, it is possible to it is clustered into Other shape.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the invention will be further described, in accompanying drawing:

Fig. 1 is the flow chart of embodiment of the present invention fuzzy entropy based on ordered information entropy space cluster analysis method.

Detailed description of the invention

In order to make the purpose of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, right The present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, not For limiting the present invention.

Present invention fuzzy entropy based on ordered information entropy space cluster analysis method, as it is shown in figure 1, mainly include following step Rapid:

S1: input normalized matrix X={x₁, x₂, x₃..., x_n, R be a fuzzy equivalence relation on X or Similarity relation, then set of relationship D={R (x, y) | x, y ∈ X}={ λ₁, λ₂, λ₃..., λ_m, 1=λ₁＞ λ₂＞ λ₃＞ ... ＞ λ_m, wherein λ_i(i=1,2,3 ..., m) for fuzzy upper spatial parameter；Make integer i=1；

S2: i-th value corresponding for set of relationship D is assigned to fuzzy entropy spatial parameter λ, λ=λ_i, initialize middle set In the middle of A, and assignment, set A is and X an equal amount of positive integer collection, A={1,2,3 ..., n}；Set C in the middle of initializing, And assignment C is empty,

S3: in the middle of order, set B is empty,Take arbitrary integer j ∈ A, B=B ∪ { x_j, A=A { x_j}；

S4: take arbitrary integer k ∈ A, if R is (x_j, x_k) >=λ, then B=B ∪ { x_j, A=A { x_j}；Take arbitrary Integer s ∈ A, if R is (x_j, x_k) >=λ, then B=B ∪ { x_s, A=A { x_s, otherwise turn S5；

S5: make C=C ∪ { B}, and make integer i+1 be assigned to i；Repeated execution of steps S2～S5, until integer i is equal to closing Assembly closes size m of D, repeats to terminate；

S6: ifThen X (λ)={ x₁, x₂, x₃... x_k..., x_λ}=C,

Calculate ordered information entropy HP (X (λ)) now (k=1,2,3,4 ..., λ)；

S7: if HP (min)=min{X (λ) }, then min=λ, turn S8, otherwise turn S2；

S8: export optimal granularity level X (min)=C.

In above-described embodiment, A, B, C are middle set."=", represents assignment, and " ∪ " represents two union of sets collection, " " table Show two quotient sets gathered.

Step S2 also exists for initial center sensitive for traditional Fuzzy C-Means Cluster Algorithm, needs to specify in advance Clusters number, and the shortcoming that correct cluster result is hardly resulted in the case of uneven for class size.This patent utilizes Set of relationship under Fuzzy Quotient Spaces replaces the Euclidean distance in traditional fuzzy C means clustering algorithm.

Step S7 utilizes criterion function ordered information entropy based on granularity thought to select an optimal level, thus Determine the number of cluster, and select there is the high sample of similarity as initial cluster center.In this step, introduce entropy computing Have amount of calculation compared with little, take the advantages such as computer storage unit is few, method is simple, it is adaptable to the cluster analysis of large sample.

Step S8 need not pre-establish cluster numbers, it appeared that the hierarchical relationship of class；Except cluster is cluster, it is also possible to It is tree-like, it is also possible to be other arbitrary shapes.

The process calculating ordered information entropy is:

If sequence X={ x_iI=1,2,3......n, use phase space reconfiguration to postpone coordinate method to either element x in X_iEnter Row phase space reconfiguration, takes m sampling point of its continuous print, obtains an x each sampled point_iM-dimensional space reconstruct vector: x_i={ x (i), x (i+1) ..., x (i+ (m-l) * l) }

Then the phase space matrix of sequence X is:When wherein m and l is respectively reconstruct dimension and postpones Between；

The reconstruct each element of vector Xi of x (i) is carried out ascending order arrangement, obtains:

X_i={ x (i+ (j₁-1)*l)≤x(i+(j₂-1)*l)≤…≤i+(j_m-1)*l}

The arrangement mode so obtained is { j₁, j₂, j₃..., j_m}

It is fully intermeshing m！In one, arranging situation occurrence numbers various to X sequence are added up, and calculate various arrangement The relative frequency that situation occurs is as its Probability p 1, p2 ... pk, k≤m！, arrangement entropy after sequence of calculation normalization:

$H=(-\underset{i=1}{\overset{k}{\Σ}}{p}_i*{\log }_2(p_i\left)\right)*{\log }_2(m!)$

It should be appreciated that for those of ordinary skills, can be improved according to the above description or be converted, And all these modifications and variations all should belong to the protection domain of claims of the present invention.

Claims (2)

1. a fuzzy entropy space cluster analysis method based on ordered information entropy, it is characterised in that comprise the following steps:

S1: input normalized matrix X={x₁, x₂, x₃..., x_n, R is a fuzzy equivalence relation on X or similar pass System, then set of relationship D={R (x, y) | x, y ∈ X}={ λ₁, λ₂, λ₃..., λ_m1=λ₁＞ λ₂＞ λ₃＞ ... ＞ λ_m, wherein λ_i(i=1,2,3 ..., m) for fuzzy upper spatial parameter；Make integer i=1；

S2: i-th value corresponding for set of relationship D is assigned to fuzzy entropy spatial parameter λ, λ=λ_i, initialize middle set A, and In the middle of assignment, set A is and X an equal amount of positive integer collection, A={1,2,3 ..., n}；Set C in the middle of initializing, and compose Value C is empty,

S3: in the middle of order, set B is empty,Take arbitrary integer j ∈ A, B=B ∪ { x_j, A=A { x_j}；

S4: take arbitrary integer k ∈ A, if R is (x_j, x_k) >=λ, then B=B ∪ { x_j, A=A { x_j}；Take arbitrary integer s ∈ A, if R is (x_j, x_k) >=λ, then B=B ∪ { x_s, A=A { x_s, otherwise turn S5；

S5: make C=C ∪ { B}, and make integer i+1 be assigned to i；Repeated execution of steps S2～S5, until integer i is equal to set of relations Close size m of D, repeat to terminate；

S6: ifThen X (λ)={ x₁, x₂, x₃... x_k..., x_λ}=C,

Calculate ordered information entropy HP (X (λ)) now (k=1,2,3,4 ..., λ)；

S7: if HP (min)=min{X (λ) }, then min=λ, turn S8, otherwise turn S2；

S8: export optimal granularity level X (min)=C.

Method the most according to claim 1, it is characterised in that calculate X (λ)={ x in step 6₁, x₂, x₃... x_k..., x_λThe ordered information entropy of }=C concretely comprises the following steps:

Phase space reconfiguration is used to postpone coordinate method to either element x in X (λ)_iCarry out phase space reconfiguration, each sampled point is taken it M sampling point of continuous print, obtains an x_iM-dimensional space reconstruct vector: x_i=x (i), x (i+1) ..., x (i+ (m-l) * L) },

Then the phase space matrix of sequence X is:Wherein m and l is respectively reconstruct dimension and time delay；

Reconstruct vector x to x (i)_iEach element carries out ascending order arrangement, obtains:

x_i={ x (i+ (j₁-1)*l)≤x(i+(j₂-1)*l)≤…≤i+(j_m-1)*l}

The arrangement mode obtained is { j₁, j₂, j₃..., j_m}

It is fully intermeshing m！In one, arranging situation occurrence numbers various to X sequence are added up, and calculate various arranging situation The relative frequency occurred is as its Probability p₁、p₂、…p_k, k≤m！, arrangement entropy after sequence of calculation normalization:

$H=(-{\mathrm{\Σ}}_{i=1}^k{p}_i*{\log }_2(p_i\left)\right)*{\log }_2\left(m!\right).$