CN106339354A - Visualization method of high-dimensional data in cloud computing network based on improved PCA - Google Patents

Abstract

The invention discloses a visualization method of high-dimensional data in a cloud computing network based on improved PCA for standardized processing of the high-dimensional data in the cloud computing network. The visualization method of high-dimensional data in the cloud computing network based on the improved PCA comprises two parts of establishment of a high-dimensional data characteristic matrix and data standardization optimization based on high-dimensional data visualization; in the process of the high-dimensional data visualization, variables in the original high-dimensional data matrix are standardized to give a new high-dimensional data characteristic matrix, characteristic values in the matrix are arranged in sequence, and principal component data of which the variances are maximum are selected; principal component contribution ratio factors and similarities of the columns are comprehensively considered in the data standardization optimization based on the high-dimensional data visualization to put forward a new data column sorting method. Simulation results show that the improved method has better visualization and classification effects, so that high-dimensional data standardization in the cloud computing network can be better realized.

Description

Methods of High-dimensional Data Visualization in system for cloud computing based on improvement pca

Technical field

The present invention relates to Methods of High-dimensional Data Visualization in a kind of system for cloud computing based on improvement pca, belong to high dimension According to standardization technical field.

Background technology

At present, with calculating developing rapidly of science and technology, high dimensional data presents the pattern of magnanimity growth.In cloud computing In network, big data is basis and the core technology of cloud computing, there is substantial amounts of high dimensional data in these big data, but currently Human cognitive ability has certain limitation it is impossible to grasp the deep information containing in high dimensional data complicated and changeable, therefore In this case, how effectively these high dimensional datas of development process become association area subject matter urgently to be resolved hurrily, High dimensional data is carried out visualize the premise being by that high dimensional data is standardized processing, determine the effect of standardization Really.And Methods of High-dimensional Data Visualization can be standardized to the variable in original high dimensional data matrix locating in system for cloud computing Reason, is set up by row again to the high dimensional data after conversion, completes high dimensional data visualization in system for cloud computing and presents, is to solve The fundamental way of the problems referred to above, causes the attention of a lot of experts and scholar.

Document [1] proposes one kind based on Methods of High-dimensional Data Visualization in the visual system for cloud computing of radial coordinate. The method estimates the intrinsic dimension of high dimensional data in system for cloud computing first with maximum likelihood principle, using less variable knot Close and blend with radial coordinate principle, on this basis dimension reduction and visualization processing is carried out to high dimensional data in system for cloud computing.Should Method is relatively simple, but there is a problem of that method limitation is big.Document [2] proposes a kind of cloud computing based on random forest Methods of High-dimensional Data Visualization in network.The method carries out supervised learning first with rf, similar between high dimensional data sample Measured, and using scatterplot, data is visualized in lower dimensional space, thus completing in system for cloud computing High dimensional data visualization presents.The method robustness is stronger, but when visualization processing is carried out to data using current algorithm, no Method eliminates high dimensional data and concentrates and comprises a large amount of irrelevant informations and redundancy, there is a problem of that data assumes error big.Document [3] Employ based on Methods of High-dimensional Data Visualization in the system for cloud computing of som.The method is first by the high dimension in system for cloud computing According to being mapped in three dimensions, using tdsom, the abscissa of point set, vertical coordinate and three variables of ordinate under three-dimensional coordinate are reflected Penetrate in the attribute classification of data set, complete high dimensional data visualization in system for cloud computing on this basis and present.The method Extensibility is stronger, but there is the defect being difficult to clearly represent high dimensional data exactly.

List of references:

[1] Xie Yonghua, Wang Chang, Yuan Fuxing. based on application in terms of cloud visualization for the Linear Octree light projecting algorithm [j]. science and technology and engineering, 2014,14 (30): 191-195.

Steel when [2]. the large-scale terrain rendering algorithm based on mipmap and emulation [j]. Computer Simulation, 2015,32 (2):270-274.

[3] Wang Jing, Xu Zhijie. real-time colony behavioral value [j] based on space-time texture. Xi'an University of Posts ＆ Telecommunications's journal, 2015,20(2):64-76.

Content of the invention

Goal of the invention: for problems of the prior art and a kind of not enough, cloud based on improvement pca of present invention proposition Methods of High-dimensional Data Visualization in calculating network, is standardized to high dimensional data in system for cloud computing processing, simulation result table Bright, improved method has preferable visualization and classifying quality, can be very good to realize high dimensional data standard in system for cloud computing Change is processed.Principal component analysiss (pca) are a kind of methods of mathematics dimensionality reduction, and its method is to find out several aggregate variables to replace originally Numerous variables, makes these aggregate variables reflect the quantity of information of primal variable as much as possible, and separate each other.

Technical scheme: Methods of High-dimensional Data Visualization in a kind of system for cloud computing based on improvement pca, to system for cloud computing Middle high dimensional data is standardized processing and optimizes；Establishment including high dimensional data eigenmatrix and visual based on high dimensional data Data normalization processes and optimizes two parts.

The establishment of high dimensional data eigenmatrix

To in high dimensional data visualization process, the variable in original high dimensional data matrix is standardized processing, gives Go out new high dimensional data eigenmatrix, the eigenvalue in matrix is arranged in order, choose the maximum number of principal components of variance According to.Specific step is as detailed below:

It is assumed that byRepresent raw data matrix under system for cloud computing, each variable that x is represented enters rower Standardization pretreatment, obtains standardized data matrix z using formula (5)

$z_{ij}=\frac{x_{i,j}-{\stackrel{\&overbar;}{x}}_i}{s_i^2}---\left(5\right)$

In formula, x_i,jRepresent j-th category attribute of i-th high dimensional data,Represent the covariance square of i-th high dimensional data Battle array,Represent the low-dimensional embedded space of i-th high dimensional data.

Formula (6) and formula (7) is then utilized to calculate

${\stackrel{\&overbar;}{x}}_i=\frac{1}{n}\underset{j=1}{\overset{n}{\σ}}{x}_{i,j}---\left(6\right)$

$s_i^2=\frac{1}{n-1}\underset{j=1}{\overset{n}{\σ}}{\left|x_{ij}-{\stackrel{\&overbar;}{x}}_i\right|}^2---\left(7\right)$

It is assumed that covariance matrix is represented by c, then calculate c using formula (8)

$c=\frac{1}{n}{z}^{t}z---\left(8\right)$

Obtain the eigenvalue matrix λ=diag (λ of c using Jacobi method₁,λ₂,…λ_m) and characteristic vector w.

The eigenvalue of each data is arranged λ according to descending order₁＞ λ₂＞ ... ＞ λ_m, and to characteristic vector row Order is adjusted correspondingly, and promotes first main constituent to have the variance of maximum, promotes second main constituent to have secondary big Variance, and minimum variance is corresponded to d-th main constituent.Choose k maximum main constituent of variance, and promote k main constituent energy Enough retain most raw information, the cumulative variance contribution of k main constituent generally making selection is more than population variance 85%, that is,It is assumed that by w_iRepresent the characteristic vector of k main constituent of selection, then utilize formula (11) Obtain k independent linear combination new variables；

${\mathrm{\ξ}}_k=\frac{w_i\×w}{d\&circleplus;({\mathrm{\λ}}_1\&greaterequal;{\mathrm{\λ}}_2\&greaterequal;...\&greaterequal;{\mathrm{\λ}}_m)}---\left(11\right)$

Can illustrate in sum, in high dimensional data visualization process, by the variable in original high dimensional data matrix It is standardized processing, provide new high dimensional data eigenmatrix, the eigenvalue in matrix is arranged in order, selection side The maximum number of principal components evidence of difference, for realizing high dimensional data visualization is laid a good foundation.

Processed based on the visual data normalization of high dimensional data and optimize

Consider similarity between principal component contributor rate factor and row it is proposed that new data row sort method, mainly Process is as follows:

It is assumed that the data matrix after main constituent conversion is represented by y, with the ξ obtaining_kIt is foundation, calculate y using formula (12)

$y=\frac{{\mathrm{\ξ}}_k}{fc}\&circletimes;{\mathrm{g\ω}}^{*}---\left(12\right)$

In formula, fc represents separating degree between the class of different classes of data, and g represents high dimensional spatial clustering data, ω^*Represent in class Concentration class.

1. the contribution degree factor calculates

First calculated row between similarity matrix be

$s=\left[\begin{array}{cccc}{s}_{11}& \mathrm{...}& & s_{1d}\\ .& & & \\ .& & & \\ .& & & \\ & & s_{ij}& \\ s_{n1}& & & s_{nd}\end{array}\right]$

Wherein s_ijRepresent the similarity of the i-th row and jth row.Then for the i-th row, and the average similarity of other all row is

$t_i=\frac{\underset{k=1}{\overset{d}{\σ}}{s}_{ik}}{d}$

t_iThe i-th row and the similarity degree of other row can be reflected, therefore can define the new contribution degree factor is

$g_i=\frac{a_i}{\underset{k=1}{\overset{d}{\σ}}{a}_k}{t}_i---\left(13\right)$

a_iRepresent contribution degree factor weights, this contribution degree factor is taken advantage of by the similarity between principal component contributor rate factor and row Amass and obtain, can preferably reflect the importance degree of each row.

2. data sorting

To g_iThe contribution degree factor representing is according to order arrangement from big to small, and will adjust it accordingly and correspond in y The order of middle row it is assumed that representing the matrix after adjustment order by y ', is then stated using formula (14)

$y^{\′}=\left\{\begin{array}{ccc}{y}_{11}^{\′}& \mathrm{...}& y_{1d}^{\′}\\ .& & .\\ .& & .\\ .& & .\\ y_{n1}^{\′}& & y_{nd}^{\′}\end{array}\right\}---\left(14\right)$

Can state out from formula (14), contribution rate is bigger, the data in y is listed in corresponding data row sequence in y ' and gets over Forward, then in visualization presents, DISPLAY ORDER is more forward.

3. data row weight

The weight size of every string of y ' is defined as contribution rate, and every for y ' string is multiplied with corresponding contribution rate, then Using formula (15) statement

$y_{new}^{\′}=\left\{\begin{array}{ccc}{g}_1{y}_{11}^{\′}& \mathrm{...}& g_1{y}_{1d}^{\′}\\ .& & .\\ .& & .\\ .& & .\\ g_n{y}_{n1}^{\′}& \mathrm{...}& g_n{y}_{nd}^{\′}\end{array}\right\}---\left(15\right)$

It is assumed that by λ_newRepresent new contribution data rate, calculate λ using formula (16)_newIn any two row i, the distance between j

${\mathrm{\λ}}_{new}(i,j)=\sqrt{d(i,j)}\×y_{new}^{\′}---\left(16\right)$

In formula, d (i, j) represents and does not add i before contribution rate factor, the distance of j.

Brief description

The data visualization effect of Fig. 1 the inventive method；

Fig. 2 is the data visualization effect of document [2] algorithm.

Specific embodiment

With reference to specific embodiment, it is further elucidated with the present invention it should be understood that these embodiments are merely to illustrate the present invention Rather than restriction the scope of the present invention, after having read the present invention, the various equivalences to the present invention for the those skilled in the art The modification of form all falls within the application claims limited range.

In carrying out high dimensional data standardization optimization process, need high dimensional data visualization in system for cloud computing On the basis of just can complete, first dimensionality reduction is carried out to whole high dimensional datas in system for cloud computing, high dimensional data is projected to two dimension On data space, extract high dimensional data and concentrate relation between classification and its feature, search different pieces of information feature permutation order and Excellent mapping, classifies to data set on this basis, completes the visualization processing to high dimensional data using its result, realizes high Data normalization process, specific step as detailed below:

It is assumed that by x_iHigh dimensional data under input cloud computing environment, x_i=(x_i1,x_i2,x_id)_tRepresent x_iD dimensional feature to Amount, then carry out dimensionality reduction using formula (1) to whole high dimensional datas in system for cloud computing, high dimensional data is projected empty to 2-D data Between on；

$\left|\right|x-w_c\left|\right|=\underset{j}{\σ}min\frac{w_j\×x_j}{x-\mathrm{\ϵ}\left(t\right)}\mathrm{\λ}\left(k\right)---\left(1\right)$

In formula, w_jRepresent the vector of whole high dimensional data identical dimensional, ε (t) representative sample data set.λ (k) representative feature Between similarity meansigma methodss, the j=1 ... in formula 1, d, x be high dimensional data matrix, w_cData matrix by wanted dimensionality reduction.

It is assumed that the similarity between high dimensional data sample, v are represented by cv (i, j)_kI () represents random high dimensional data feature Vector, then utilize formula (2) to extract high dimensional data and concentrate the relation between classification and its feature

$prox=\frac{cv(i,j)\&circletimes;v_k\left(i\right)}{\left|\right|x-w_c\left|\right|\·{\mathrm{cv}}_{n\×n}}---\left(2\right)$

In formula, cv_n×nRepresent the transformation matrix of high dimensional data.

It is assumed that by cv_n×nRepresent the transformation matrix of high dimensional data,Represent the eigenvalue of dissimilar high dimensional data, full It is sufficient to the condition of (k=1,2,3...), then search different pieces of information feature permutation order and optimum mapping, set up high using formula (3) The Visualization Model of dimension data

In formula, similarity between prox (i, j) representative sample (i, j), the meansigma methodss of similarity between λ (k) representative feature.

With formula (3) as foundation, whole High Dimensional Data Sets is standardized process using formula (4)

$\hat{m}\left(k\right)=\frac{prox\·cv(i,j)}{w_{\left(\mathrm{\ξ}\right)}}---\left(4\right)$

But traditional method can not effectively eliminate redundant data and information, effect of visualization is poor, reduces data normalization The effect processing.Methods of High-dimensional Data Visualization in a kind of system for cloud computing based on improvement pca is proposed, in system for cloud computing High dimensional data is standardized processing and optimizes；Establishment including high dimensional data eigenmatrix and be based on the visual number of high dimensional data Optimize two parts according to standardization.

The establishment of high dimensional data eigenmatrix

To in high dimensional data visualization process, the variable in original high dimensional data matrix is standardized processing, gives Go out new high dimensional data eigenmatrix, the eigenvalue in matrix is arranged in order, choose the maximum number of principal components of variance According to.Specific step is as detailed below:

It is assumed that byRepresent raw data matrix under system for cloud computing, each variable that x is represented enters rower Standardization pretreatment, obtains standardized data matrix using formula (5)

$z_{i,j}=\frac{x_{i,j}-{\stackrel{\&overbar;}{x}}_i}{s_i^2}---\left(5\right)$

In formula, x_i,jRepresent j-th category attribute of i-th high dimensional data,Represent the covariance square of i-th high dimensional data Battle array,Represent the low-dimensional embedded space of i-th high dimensional data.

Formula (6) and formula (7) is then utilized to calculate

${\stackrel{\&overbar;}{x}}_i=\frac{1}{n}\underset{j=1}{\overset{n}{\σ}}{x}_{i,j}---\left(6\right)$

$s_i^2=\frac{1}{n-1}\underset{j=1}{\overset{n}{\σ}}{\left|x_{ij}-{\stackrel{\&overbar;}{x}}_i\right|}^2---\left(7\right)$

It is assumed that covariance matrix is represented by c, then calculate c using formula (8)

$c=\frac{1}{n}{z}^{t}z---\left(8\right)$

Obtain the eigenvalue matrix λ=diag (λ of c using Jacobi method₁,λ₂,...λ_m) and characteristic vector w.

By described above, the eigenvalue of each data is arranged λ according to order₁＞ λ₂＞ ... ＞ λ_m, and to characteristic vector The order of row is adjusted correspondingly, and promotes first main constituent to have the variance of maximum, promotes second main constituent to have secondary Big variance, and minimum variance is corresponded to d-th main constituent.Choose k maximum main constituent of variance, and promote k main one-tenth Divide and can retain most raw information, the cumulative variance contribution of k main constituent generally making selection is more than always side The 85% of difference, that is,It is assumed that by w_iRepresent the characteristic vector of k main constituent of selection, then utilize formula (11) obtain k independent linear combination new variables；

${\mathrm{\ξ}}_k=\frac{w_i\×w}{d\&circleplus;({\mathrm{\λ}}_1\&greaterequal;{\mathrm{\λ}}_2\&greaterequal;...\&greaterequal;{\mathrm{\λ}}_m)}---\left(11\right)$

Can illustrate in sum, in high dimensional data visualization process, by the variable in original high dimensional data matrix It is standardized processing, provide new high dimensional data eigenmatrix, the eigenvalue in matrix is arranged in order, selection side The maximum number of principal components evidence of difference, for realizing high dimensional data visualization is laid a good foundation.

Processed based on the visual data normalization of high dimensional data and optimize

Consider similarity between principal component contributor rate factor and row it is proposed that new data row sort method, mainly Process is as follows: it is assumed that representing the data matrix after main constituent conversion by y, with the ξ obtaining_kIt is foundation, calculated using formula (12) y

$y=\frac{{\mathrm{\ξ}}_k}{fc}\&circletimes;{\mathrm{g\ω}}^{*}---\left(12\right)$

In formula, fc represents separating degree between the class of different classes of data, and g represents high dimensional spatial clustering data, ω^*Represent in class Concentration class.

1. the contribution degree factor calculates

First calculated row between similarity matrix be

$s=\left[\begin{array}{cccc}{s}_{11}& \mathrm{...}& & s_{1d}\\ .& & & \\ .& & & \\ .& & & \\ & & s_{ij}& \\ s_{n1}& & & s_{nd}\end{array}\right]$

Wherein s_ijRepresent the similarity of the i-th row and jth row.Then for the i-th row, and the average similarity of other all row is

$t_i=\frac{\underset{k=1}{\overset{d}{\σ}}{s}_{ik}}{d}$

t_iThe i-th row and the similarity degree of other row can be reflected, therefore can define the new contribution degree factor is

$g_i=\frac{a_i}{\underset{k=1}{\overset{d}{\σ}}{a}_k}{t}_i---\left(13\right)$

In formula, a_iRepresent contribution degree factor weights, this contribution degree factor is by similar between principal component contributor rate factor and row The product of degree obtains, and can preferably reflect the importance degree of each row.

2. data sorting

To g_iThe contribution degree factor representing is according to order arrangement from big to small, and will adjust it accordingly and correspond in y The order of middle row it is assumed that representing the matrix after adjustment order by y ', is then stated using formula (14)

$y^{\′}=\left\{\begin{array}{ccc}{y}_{11}^{\′}& \mathrm{...}& y_{1d}^{\′}\\ .& & .\\ .& & .\\ .& & .\\ y_{n1}^{\′}& & y_{nd}^{\′}\end{array}\right\}---\left(14\right)$

Can state out from formula (14), contribution rate is bigger, the data in y is listed in corresponding data row sequence in y ' and gets over Forward, then in visualization presents, DISPLAY ORDER is more forward.

3. data row weight

1) the weight size of every string of y ' is defined as contribution rate, and every for y ' string is multiplied with corresponding contribution rate, Formula (15) is then utilized to state

$y_{new}^{\′}=\left\{\begin{array}{ccc}{g}_1{y}_{11}^{\′}& \mathrm{...}& g_1{y}_{1d}^{\′}\\ .& & .\\ .& & .\\ .& & .\\ g_n{y}_{n1}^{\′}& \mathrm{...}& g_n{y}_{nd}^{\′}\end{array}\right\}---\left(15\right)$

It is assumed that by λ_newRepresent new contribution data rate, calculate λ using formula (16)_newIn any two row i, the distance between j

${\mathrm{\λ}}_{new}(i,j)=\sqrt{d(i,j)}\×y_{new}^{\′}---\left(16\right)$

In formula, d (i, j) represents and does not add i before contribution rate factor, the distance of j.

Emulation proves

In order to prove that in the system for cloud computing based on improvement pca proposing, Methods of High-dimensional Data Visualization carries out high dimensional data The effectiveness of standardization, needs once to be tested.The hardware system that experiment is chosen is 2.8ghz cpu, the meter of 1g internal memory Calculation machine, the data set in experiment derives fromhttp://dbgroup.cs.tsinghua.edu download.Selected data collection is through conventional The Performance comparision of various pattern recognition task in document, table 1 provides sample number, characteristic number and the classification number of experimental data set.

Table 1 experimental data set information

Wherein, nd represents data name, ns representative sample number, cs representative feature number, and nc represents classification number,

In order to ensure the fairness of high dimensional data visualized experiment, the estimation of grader error rate adopts 6v, takes 6 independences The average result of experiment, 11v refers to for data set sample to be divided into into 6 parts.Because the good and bad directly shadow data mark of effect of visualization Standardization processes effect of optimization, and therefore the present invention to high dimensional data, verify by visual effect.

Algorithms of different classification error rate

It is respectively adopted this paper algorithm and document [2], document [1] algorithm carry out high dimensional data in system for cloud computing and visualize in fact Test.The high dimensional data classification error rate of relatively 3 kinds of algorithms of different, comparing result is shown in Table 2.

Table 2 algorithms of different classification error rate contrasts

Wherein, nd represents data name, and pa represents the error rate of the inventive method, and la [9] represents the mistake of document [2] algorithm Rate by mistake, la [8] represents the error rate of document [1] algorithm.

Can analyze from table 2 and draw, carry out high dimensional data visualization classification in system for cloud computing using the inventive method Error rate carry out the mistake of high dimensional data visualization classification in system for cloud computing well below document [2], document [1] algorithm Rate, this is primarily due to when carrying out high dimensional data visualization using this paper algorithm, after being changed with principal component contributor rate High dimensional data column pitch is from again being set up by row to the high dimensional data after conversion using hierarchical clustering algorithm, thus having ensured this Inventive method carries out the accuracy that high dimensional data in system for cloud computing visualizes data classification.

Algorithms of different carries out the visual Contrast on effect of high dimensional data

It is respectively adopted the inventive method and document [2] carries out high dimensional data visualized experiment in system for cloud computing.Relatively 2 kinds The high dimensional data effect of visualization of algorithms of different.Comparing result is shown in Fig. 1 and Fig. 2.

Analyze from Fig. 1 and Fig. 2 and can draw, carry out high dimensional data visualization in system for cloud computing using the inventive method Effect be better than document [2] and carry out the visual effect of high dimensional data, this is primarily due to carrying out higher-dimension using document [2] During data visualization, first the variable in original high dimensional data matrix is standardized processing, provides new high dimensional data feature Matrix, the eigenvalue in matrix is arranged in order, chooses variance maximum number of principal components evidence, thus having ensured side of the present invention Method carries out the visual superiority of high dimensional data.

Simulation result shows, institute's extracting method has preferable visualization and classifying quality.

Claims (3)

1. a kind of based on improve pca system for cloud computing in Methods of High-dimensional Data Visualization it is characterised in that: to system for cloud computing Middle high dimensional data is standardized processing and optimizes；Establishment including high dimensional data eigenmatrix and visual based on high dimensional data Data normalization processes and optimizes two parts；

The establishment of high dimensional data eigenmatrix

To in high dimensional data visualization process, the variable in original high dimensional data matrix is standardized processing, is given new High dimensional data eigenmatrix, the eigenvalue in matrix is arranged in order, is chosen the maximum number of principal components evidence of variance；

Processed based on the visual data normalization of high dimensional data and optimize

Consider similarity between principal component contributor rate factor and row it is proposed that new data row sort method.

2. Methods of High-dimensional Data Visualization in the system for cloud computing based on improvement pca as claimed in claim 1, its feature exists In:

The establishment of high dimensional data eigenmatrix, specific step as detailed below:

It is assumed that byRepresent raw data matrix under system for cloud computing, each variable that x is represented is standardized Pretreatment, obtains standardized data matrix z using formula (5)

$z_{i,j}=\frac{x_{i,j}-\stackrel{\&overbar;}{x_i}}{s_i^2}---\left(5\right)$

In formula, x_i,jRepresent j-th category attribute of i-th high dimensional data,Represent the covariance matrix of i-th high dimensional data,Represent the low-dimensional embedded space of i-th high dimensional data；

Formula (6) and formula (7) is then utilized to calculate

${\stackrel{\&overbar;}{x}}_i=\frac{1}{n}\underset{j=1}{\overset{n}{\σ}}{x}_{i,j}---\left(6\right)$

$s_i^2=\frac{1}{n-1}\underset{j=1}{\overset{n}{\σ}}|x_{ij}-{\stackrel{\&overbar;}{x}}_i{|}^2---\left(7\right)$

It is assumed that covariance matrix is represented by c, then calculate c using formula (8)

$c=\frac{1}{n}{z}^{t}z---\left(8\right)$

Obtain the eigenvalue matrix λ=diag (λ of c using Jacobi method₁,λ₂,...λ_m) and characteristic vector w；

The eigenvalue of each data is arranged λ according to descending order₁＞ λ₂＞ ... ＞ λ_m, and the order to characteristic vector row It is adjusted correspondingly, promotes first main constituent to have the variance of maximum, promote second main constituent to have secondary big variance, And minimum variance is corresponded to d-th main constituent；Choose k maximum main constituent of variance, and promote k main constituent can retain Most raw information；It is assumed that by w_iRepresent the characteristic vector of k main constituent of selection, then obtain k solely using formula (11) Vertical linear combination new variables:

${\mathrm{\ξ}}_k=\frac{w_i\×w}{d\&circleplus;({\mathrm{\λ}}_1\&greaterequal;{\mathrm{\λ}}_2\&greaterequal;...\&greaterequal;{\mathrm{\λ}}_m)}---\left(11\right).$

3. Methods of High-dimensional Data Visualization in the system for cloud computing based on improvement pca as claimed in claim 2, its feature exists In: processed based on the visual data normalization of high dimensional data and optimize, main process is as follows:

It is assumed that the data matrix after main constituent conversion is represented by y, with the ξ obtaining_kIt is foundation, calculate y using formula (12)

$y=\frac{{\mathrm{\ξ}}_k}{fc}\&circletimes;{\mathrm{g\ω}}^{*}---\left(12\right)$

In formula, fc represents separating degree between the class of different classes of data, and g represents high dimensional spatial clustering data, ω^*Represent in class and assemble Degree.

(1) the contribution degree factor calculates

First calculated row between similarity matrix be

$s=\left[\begin{array}{cccc}{s}_{11}& ...& & s_{1d}\\ .& & & \\ .& & & \\ .& & & \\ & & s_{ij}& \\ s_{n1}& & & s_{nd}\end{array}\right]$

Wherein s_ijRepresent the similarity of the i-th row and jth row.Then for the i-th row, and the average similarity of other all row is

$t_i=\frac{\underset{k=1}{\overset{d}{\σ}}{s}_{ik}}{d}$

t_iThe i-th row and the similarity degree of other row can be reflected, therefore can define the new contribution degree factor is

$g_i=\frac{a_i}{\underset{k=1}{\overset{d}{\σ}}{a}_k}{t}_i---\left(13\right)$

a_iRepresent contribution degree factor weights, this contribution degree factor is obtained by the product of the similarity between principal component contributor rate factor and row Arrive, can preferably reflect the importance degree of each row；

(2) data sorting

To g_iThe contribution degree factor representing is according to order arrangement from big to small, and will adjust it accordingly and correspond to row in y Order it is assumed that representing the matrix after adjustment order by y ', is then stated using formula (14)

$y^{\′}=\left\{\begin{array}{ccc}{y}_{11}^{\′}& ...& y_{1d}^{\′}\\ .& & .\\ .& & .\\ .& & .\\ y_{n1}^{\′}& & y_{nd}^{\′}\end{array}\right\}---\left(14\right)$

Can state out from formula (14), contribution rate is bigger, the data in y is listed in corresponding data row sequence in y ' and more leans on Before, then in visualization presents, DISPLAY ORDER is more forward；

(3) data row weight

The weight size of every string of y ' is defined as contribution rate, and every for y ' string is multiplied with corresponding contribution rate, then utilize Formula (15) is stated

$y_{new}^{\′}=\left\{\begin{array}{ccc}{g}_1{y}_{11}^{\′}& ...& g_1{y}_{1d}^{\′}\\ .& & .\\ .& & .\\ .& & .\\ g_n{y}_{n1}^{\′}& ...& g_n{y}_{nd}^{\′}\end{array}\right\}---\left(15\right)$

It is assumed that by λ_newRepresent new contribution data rate, calculate λ using formula (16)_newIn any two row i, the distance between j

${\mathrm{\λ}}_{new}(i,j)=\sqrt{d(i,j)}\×y_{new}^{\′}---\left(16\right)$

In formula, d (i, j) represents and does not add i before contribution rate factor, the distance of j.