CN104008383B - Based on manifold learning linearizing high spectrum image feature extracting method - Google Patents
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Abstract
One kind is based on manifold learning linearizing high spectrum image feature extracting method, belongs to hyperspectral image data and processes and applied technical field.The present invention is directed to the deficiency of manifold learning no generalization ability it is proposed that a kind of improved manifold learning linearization technique.Methods described comprises the steps：First, preliminary dimensionality reduction result and Laplacian Matrix are calculated；2nd, Matrix division constant term matrix and coefficient matrix are built；3rd, calculate Feature Conversion matrix；4th, pass through Feature Conversion matrix calculus final dimensionality reduction result.The present invention is directed to the hypothesis of overall Linear Mapping in LPP, NPE and LLTSA linearisation manifold learning in many times invalid deficiency, the penalty term deviateing former manifold learning result is added in original cost function, and cast out the bound term in former object function, the solution of optimal characteristics transition matrix has been converted to the Solve problems of a Matrix division.The method is applied to the feature extraction of high spectrum image.
Description
Technical field
The invention belongs to hyperspectral image data is processed and applied technical field, it is related to a kind of high spectrum image feature and extracts
Method is and in particular to a kind of be based on manifold learning linearizing high spectrum image feature extracting method.
Background technology
High-spectrum seems the huge data cube of quantity of information, and each pixel corresponds to one and comprises up to a hundred wave bands
Spectral line, this studies the relation between material and the curve of spectrum for people and provides possibility.But it is superfluous to there is data in high-spectral data
Remaining and dimension disaster problem, people have urgent demand to go to eliminate the redundancy of this information of high-spectral data.EO-1 hyperion number
According to the dependency that is mainly between high-spectral data wave band of this redundancy cause, dimensionality reduction is a kind of important pretreatment side
Method, although as PCA (Principal Component Analysis) and LDA (Linear Discriminant Analysis)
Such linear dimension reduction method is realized simply, but high spectrum image has nonlinear characteristic, and manifold learning can be more preferable
Ground excavates the nonlinear organization of high-spectral data, improves data analysis capabilities.Classical manifold learning has LE
(Laplacian Egenmap), LLE (Locally Linear Embedding) and LTSA (Local Tangent Space
Alignment) method, can be used for the feature extracting method of high spectrum image.
But classical manifold learning such as LE no generalization ability, when there being new EO-1 hyperion sample data to occur, only
New sample data and original sample data are combined together and carry out overall study again and just can access new sample
The dimensionality reduction result of notebook data.When the number of new sample data seems little compared to the number of original sample data
Wait it is clear that so repeating the time complexity that large-scale calculating can greatly increase method.For hyperspectral classification demand, stream
Shape learning method must possess generalization ability, because many times training data and test data to be sorted cannot be placed on one
Rise and learnt, in this case, the feature that test data to be sorted has to be mapped to low-dimensional by extensive method is empty
Between, otherwise will be unable to the feature space in low-dimensional and new high-spectral data is classified.
Although linear dimension reduction method such as PCA etc. has in process, and nonlinear effect data is not good, they but can
Obtain an overall mapping function, thus possess generalization ability.Manifold learning linearisation is solved flow for this lot of scholar
The problem of shape study no generalization ability.It is exactly typically very wherein the linearisation to LE, LLE, LTSA, respectively obtain LPP
(Locality preserving projections)、NPE(Neighborhood Preserving Embedding)、
LLTSA(Linear Local Tangent Space Alignment).
Manifold learning possesses unified framework, for the manifold learning side based on spectral factorization such as such as LE, LLE and LTSA
For method, dimensionality reduction result Y of optimum*Can be solved by following optimization problem：
Wherein tr () is the mark operator seeking matrix, and L is Laplacian Matrix, and B is constraint matrix.LPP, NPE and
LLTSA assumes that one overall Linear Mapping of presence in reduction process：
Y=VTX (2),
Optimization problem in formula (1) is changed into：
Obtain the Linear Mapping matrix V of optimum*Afterwards, whether new sample or old sample, can pass through
Formula (2) is mapped to dimension reduction space.But this hypothesis of formula (2) is invalid many times.In order to obtain the linear of the overall situation
Mapping, these methods are that the local retention performance to script method has done certain compromise in fact.
Content of the invention
The present invention is directed to the deficiency of manifold learning no generalization ability it is proposed that a kind of improved manifold learning linearisation
Method, and use it for the feature extracting method of high spectrum image.
The purpose of the present invention is achieved through the following technical solutions：
So that linearizing process must not sacrifice the ability that former manifold learning keeps local characteristicses as far as possible, this
Invention adds the penalty term deviateing former manifold learning result in original cost function so that optimization in formula (3)
Problem is changed into：
Wherein YLThe dimensionality reduction result having learnt, α is penalty coefficient, can by LE, LLE, LTSA or other
But a kind of what respond well manifold learning not possessing generalization ability obtains.Compared to formula (3), formula (4) is no longer necessary to
Add bound term VTXBXTV=I, this makes the region of search of optimization problem be widened, it is possible to obtain than traditional dimension reduction method more
Good dimensionality reduction effect.This extensive method is based on YLKnown go to ask for the process of a linearisation mapping matrix V, be a kind of complete
The linear regression method of office.Original manifold learning is all the dimensionality reduction result obtaining optimum by feature decomposition, this
The improved method of bright proposition obtains the dimensionality reduction result of optimum by solving a matrix equation.
Here provide the solution procedure to the optimization problem in (4)：
Cost function g (V) obtains to V derivation：
Wherein A=α I+L.
Then the optimization problem in formula (4) is changed into the problem of a solution matrix equation：
[XAXT] V=α XYL T(7).
It is equivalent to following system of linear equations problem:
So having：
Formula (9) is a function expression, and wherein vec () is matrix-vector operator, for vec (B), will D
The matrix conversion of × d dimension is D × d dimensional vector.Avec () is moment of a vector array operator.For the matrix of D × d dimension, vec
The operational rule of () is the column vector that the element of every for matrix a line is converted to d dimension, and the row after every row is changed
Vector line up D × d dimensional vector according to line number, avec () is then its inverse operation, will D × d dimension column vector be converted to D
× d ties up matrix.
To (9), abbreviation obtains further：
V=(XAXT)-1B (10).
The present invention provide based on manifold learning linearizing high spectrum image feature extracting method, comprise the following steps that：
Step one：Calculate preliminary dimensionality reduction result and Laplacian Matrix.
Given high-spectral data collection X, X are D × N-dimensional matrixes, and D is data dimension, and N is number of samples, and d is dimensionality reduction dimension,
A certain manifold learning in execution such as LE, LLE and LTSA method, obtains preliminary dimensionality reduction result Y of this methodLWith
Laplacian Matrix L, wherein YLIt is d × N-dimensional matrix, L is N × N-dimensional matrix.
Step 2：Build Matrix division constant term matrix and coefficient matrix.
The linearizing manifold learning such as LPP, NPE and LLTSA generally will be by the Laplacian Matrix L spy to N × N-dimensional
Levy to decompose to obtain the Feature Conversion matrix of optimum, computationally intensive, the innovative point of this step is optimal characteristics transition matrix
Solution be converted to the Solve problems of a Matrix division.
Shown in Matrix division such as formula (7), provide the structure formula of constant term matrix and coefficient matrix here：
1) build the Matrix division constant term matrix B of D × d dimension：
B=α XYL T,
Wherein α is the penalty coefficient that is positive number, and acquiescence may be configured as 1.
2) build the Matrix division coefficient matrix C of D × D dimension：
C=X (α I+L) XT,
Wherein, I is the unit matrix of N × N-dimensional.
Step 3：Calculate Feature Conversion matrix.
In the solution procedure of Matrix division, generally matrix to be carried out with vectorization and matrixing fortune is carried out to vector
Calculate, and also relate to existence and unigueness, these computings make the internal memory of the solution time big consumption of Matrix division
Space is also big.The innovative point of this step is that the problem reduction solving Matrix division to be realized for two matrix multiples, real
Now facilitate, method complexity is little.
1) equation system matrix number C is carried out inverting obtaining matrix H：
H=C-1；
2) pass through matrix H Feature Conversion matrix V mutually multiplied with equation group constant term matrix B：
V=HB.
Step 4：By Feature Conversion matrix calculus final dimensionality reduction result：
Y=VTX,
Wherein, Y is final dimensionality reduction result.
The beneficial effects of the present invention is：
1st, this method is a kind of linear regression method of the overall situation, so that any one does not possess the stream of generalization ability
After shape learning method carries out linearisation by the method, obtain generalization ability, and can obtain than traditional dimension reduction method more
Good feature extraction effect.
2nd, the hypothesis being directed to overall Linear Mapping in LPP, NPE and LLTSA linearisation manifold learning is many times
Invalid deficiency, adds the penalty term deviateing former manifold learning result in original cost function, and casts out
Bound term in former object function, this makes the region of search of optimization problem be expanded, it is possible to obtain than traditional dimensionality reduction side
Method more preferable dimensionality reduction effect.
Brief description
Fig. 1 is flow chart of steps of the present invention；
Fig. 2 is the feature scatterplot of the hyperspectral image data in the present invention；
Fig. 3 be based on the feature extraction of the present invention after high spectrum image nicety of grading.
Specific embodiment
Below in conjunction with the accompanying drawings technical scheme is further described, but does not limit to so, every to this
Inventive technique scheme is modified or equivalent, without deviating from the spirit and scope of technical solution of the present invention, all should cover
In protection scope of the present invention.
The present invention needs to obtain Laplacian Matrix with just using a kind of existing manifold learning in the first step
The dimensionality reduction result of step, here taking LLE method as a example, as the manifold learning in first step, then using this
Bright proposed method carries out feature extraction to high spectrum image.Experiment selects IND PINE EO-1 hyperion with hyperspectral image data
Image, this high-spectrum seems to be taken pictures in a farmland to Indiana, USA by the Kennedy Space Center of the U.S.
And obtain, in diagram picture, one has 16 kinds of different crops, and the spatial resolution of image is 20 × 20m2, each pixel has
224 wave bands, cover the spectral range that spectral region is 0.2～2.4 μm, and spectral resolution is 10nm.
From IND PINE high spectrum image, randomly select 1500 pixels as training sample, randomly from residue
Sample in select 1500 pixels as test sample.In the present embodiment, using the present invention, training sample is learnt,
Obtain Feature Conversion matrix, then using Feature Conversion matrix, feature extraction is carried out to test sample, and use KNN grader
Test sample is classified.In order to verify feature of present invention extract ground effectiveness, to same training data, test data and
Grader, simultaneously using the linearization technique NPE method as a comparison that LLE is classical.
As shown in figure 1, comprising the following steps that of feature extraction is carried out using the present invention：
Step one：Dimensionality reduction result Y is obtained by LLE manifold learningLWith Laplacian Matrix L.
1) input training setWherein each sample data dimension is 224, test specimens
This number is 1500；The number in setting neighbour domain is 20；Setting dimensionality reduction result dimension 30.
2) find neighborhood collection
To each sample x in training seti, wherein i represents xiLocation index number in training sample set X, i=1,
2 ..., 1500, by sample between Euclidean distance sequence, search training set in xi20 nearest samples, constitute sample xi's
Neighborhood collection
3) build reconstruction coefficients matrix W：
Wherein：WijFor xjTo xiReconstruction coefficients, xjIt is the test sample of j for position call number in training sample set X, its
In, T (xj,Xi) calculated by formula below：
Wherein：index(xj,Xi) represent xjIn XiMiddle location index, that T calculates is index (x in matrix Pj,Xi) arrange
The sum of all elements；Matrix P is neighborhood collection XiLocal covariance matrix inverse, can be calculated by formula below：
P=[(Xi-xi)T(Xi-xi)]-1,
Wherein：S is the sum of all elements of matrix P, can be calculated by formula below：
4) build Laplacian Matrix：
L=(I-W)T(I-W),
Wherein：I is N × N-dimensional unit matrix.
5) carry out feature decomposition：
Lz=λ z.
6) obtain preliminary dimensionality reduction result：
Wherein：ziiIt is the little corresponding characteristic vector of eigenvalue of i-th i of L, ii=2 ..., d+1.
Step 2：Build Matrix division constant term matrix B and coefficient matrix C.
1) positive number penalty coefficient α is set, is set to α=1 here.
2) Matrix division constant term matrix B is calculated by formula below：
B=α XYL T.
3) Matrix division coefficient matrix C is calculated by formula below：
C=X (α I+L) XT.
Step 3：Calculate Feature Conversion matrix V.
1) equation system matrix number C is carried out inverting obtaining matrix H：
H=C-1.
2) pass through matrix H Feature Conversion matrix V mutually multiplied with equation group constant term matrix B：
V=HB.
Step 4：By Feature Conversion matrix calculus final dimensionality reduction result.
1) final dimensionality reduction result Y of training set is calculated by formula below：
Y=(V)TX.
2) the final dimensionality reduction result of test set is calculated by formula below
Wherein：For test sample collection.
The final dimensionality reduction result of test set and training set is as shown in Figure 2.The extensive result of new samples as we can see from the figure
Basically identical with the dimensionality reduction result of test sample it is known that the extensive effect of the carried feature extracting method of the present invention is preferable.
Step 5：Using KNN sorting technique, class test is carried out to test sample.
1) calculate the final dimensionality reduction result of test sample collectionIn each test sample and all training sample sets final
The Euclidean distance of dimensionality reduction result Y.
2) take closest 5 training sample as the neighbour of test sample.
3) primary categories according to this 5 neighbour's ownership, test sample is classified.
4) calculate the accuracy of classification.
Classification accuracy rate is as shown in Figure 3.As can see from Figure 3 bloom is carried out by the carried feature extracting method of the present invention
The extensive of spectrogram picture has higher overall nicety of grading by KNN classification afterwards, and the nicety of grading of LLE-GLR method substantially will
Higher than the nicety of grading of LLE, NPE method, the feature extracting method proposing in this explanation present invention is conducive to improving high-spectrum
The nicety of grading of picture.
The above analysis it is known that proposed by the present invention based on manifold learning linearizing high spectrum image feature extraction side
Method, is improved really to existing manifold learning linearization technique.The feature extracting method proposing in the present invention can have
The classification essence solving the deficiency that existing manifold learning cannot learn to new samples, high spectrum image can also being improved simultaneously of effect
Degree, has very big engineering real value.
Claims (1)
1. a kind of based on manifold learning linearizing high spectrum image feature extracting method it is characterised in that described high spectrum image
Feature extracting method step is as follows：
First, give high-spectral data collection X, preliminary dimensionality reduction result Y is obtained by manifold learningLWith Laplacian Matrix L, its
Middle X is D × N-dimensional matrix, and D is data dimension, and N is number of samples, YLIt is d × N-dimensional matrix, L is N × N-dimensional matrix, and d is dimensionality reduction
Dimension；
2nd, Matrix division constant term matrix B and coefficient matrix C are built：
1) build the Matrix division constant term matrix B of D × d dimension：
B=α XYL T,
Wherein, α is the penalty coefficient that is positive number；
2) build the Matrix division coefficient matrix C of D × D dimension：
C=X (α I+L) XT,
Wherein, I is the unit matrix of N × N-dimensional；
3rd, calculate Feature Conversion matrix：
1) Matrix division coefficient matrix C is carried out inverting obtaining matrix H：
H=C-1；
2) pass through matrix H Feature Conversion matrix V mutually multiplied with Matrix division constant term matrix B：
V=HB；
4th, pass through Feature Conversion matrix calculus final dimensionality reduction result：
Y=VTX,
Wherein, Y is final dimensionality reduction result.
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