CN103198331B - Multiple spectrogram characteristic amalgamation and recognition method based on analysis of PCA-LDA - Google Patents

Abstract

The invention discloses a multiple spectrogram characteristic amalgamation and recognition method based on analysis of PCA-LDA. The multiple spectrogram characteristic amalgamation and recognition method based on analysis of the PCA-LDA comprises the following steps: utilizing a PCA-LDA method to extract spectrogram characteristics of all samples; amalgamating the extracted spectrogram characteristics of all the samples to a multiple spectrogram characteristics amalgamation matrix; establishing a multiple spectrogram amalgamation SVM classifier; and utilizing multiple spectrogram amalgamation SVM classifier samples to recognize. The multiple spectrogram characteristic amalgamation and recognition method based on analysis of PCA-LDA can quickly conduct accurate analytical recognition to the integral characteristic of complex mixture.

Description

Many spectrograms Feature Fusion recognition methodss based on PCA_LDA analysis

Technical field

The present invention relates to a kind of many spectrograms Feature Fusion recognition methodss based on PCA_LDA analysis, particularly a kind of quick Complex mixture global feature spectrum analysis method.

Background technology

Pattern recognition is widely used in respectively with reference to analytical technologies such as spectrum, chromatograph, ion mobility spectrometry, mass spectrum, nuclear magnetic resonance, NMR On based food quality control.Raman spectrum is a kind of scattering spectrum.Raman spectrum analyses method is to be drawn based on India scientist C.V. Graceful found Raman scattering effect, is analyzed to the scattering spectrum different from incident light frequency to obtain molecular vibration, to turn Dynamic aspect information, and it is applied to a kind of analysis method of molecular structure research.Being mainly characterized by of Raman spectrum be quick, simple, Sample is reproducible without pre-treatment, signal.Additionally due to the Raman scattering of water is very faint, therefore Raman spectrum can carry out water Material measurement detection in solution, greatly expands and carries out studying detection range.

Ion mobility spectrometry is that a kind of new gas phase occurring in early 1970s separates and detection technique.It is with ion The difference of drift time is qualitative come the separation to carry out ion, by the concept similar to chromatographic retention, is originally referred to as Gas ions chromatograph.Ion mobility spectrometry is a kind of efficient separate analytical technique, have been widely used petrochemical industry, environmental analyses, The fields such as food analyses.Mass spectrum is a kind of analysis side being analyzed by the mensure of the mass-to-charge ratio to sample ion Method.Because mass spectral analyses have, sensitivity is high, and amount of samples is few, and analyze speed is fast, separates and identifies the advantages of simultaneously carry out, because This, mass-spectrometric technique is also widely used in chemical, environmental analyses, the field such as medicine analysis.

With the quick change of fake and forged technology, all kinds of in current China public product particularly Safety of Food Quality Risk is increasingly increased with suffering, increasingly urgent to the demand of the science of Product quality and safety information, quick obtaining technology and equipment. In recent years, a series of food safety malignant events of interior particularly domestic generation at the international level, show to take with a certain item or A few eigenvalues of person come also more and more significant the drawbacks of judging product quality, carry out qualitative, quantitative using Global Information to product Judge becoming the focus of research.

For complicated chemical combination objects system, individual spectrogram is difficult to comprehensively reflect the Chemical Characteristics of product, needs It is combined many spectrogram information, will reflect that the different semiochemical various spectrogram information of product merge, comprehensive characterization product Chemical composition characteristic so that various information carries out effectively complementary, strengthen the trust degree of data, improve precision of prediction, can By property and robustness, this judges there is important Research Significance to the Global Information of food.Although the grinding of many spectrograms information fusion Study carefully and achieve certain achievement, in color-analytical tool such as matter combination, GC-FTIR, have some simple data fusion, but Mass spectrum, infrared spectrum are depended on to material entirety qualitative/quantitative judgement aspect.Do not realize spectrogram information inside combined system Merge, be more not carried out the information fusion between different combined systems.

Content of the invention

The technical problem to be solved is to overcome the deficiencies in the prior art, provides one kind can be quickly to multiple Hybrid compound global feature is accurately analyzed the many spectrograms Feature Fusion recognition methodss based on PCA_LDA analysis of identification.

The present invention specifically employs the following technical solutions solution above-mentioned technical problem：The present invention devises one kind and is based on PCA_ Many spectrograms Feature Fusion recognition methodss of LDA analysis, comprise the following specific steps that：

Step（1）：N sample of collection, sets n sample and belongs to c kind classification, and each sample is chosen with m different spectrum Figure, using PCA_LDA method extract all samples chromatogram characteristic, and by extract all samples chromatogram characteristic be fused to many Spectrum fusion feature matrix；

Step（2）：Using step（1）In multispectral fusion feature matrix set up multispectral fusion SVM classifier；

Step（3）：Using step（2）The multispectral fusion SVM classifier of middle foundation is to step（1）The sample of middle collection is carried out Identification.

A kind of optimization method as the present invention：Described step（1）Including specifically processing as follows：

Step（11）：The training sample set data of i-th sample of labelling isThe m dimension data collection vector of i-th sample ForThen n × m raw data matrix of all samples isWherein, i=1,2, 3 ... n, l_iIt is defined asClass label；

Step（12）：Using step（11）In raw data matrix X and equation below calculate class in mean dispersion error matrix Sw：

$S_w=\underset{g=1}{\overset{c}{\mathrm{\Σ}}}\underset{p=1}{\overset{n_g}{\mathrm{\Σ}}}{({\stackrel{\→}{x}}_p^g-{\stackrel{\→}{t}}_x^g)}^T\·({\stackrel{\→}{x}}_p^g-{\stackrel{\→}{t}}_x^g)$

Wherein, n_gRepresent the number of samples of g class,It is defined as the mean vector of the sample of g class, g=1,2,3 ... c,It is defined as the vector of p-th sample in g class sample, T is defined as matrix transpose, p=1,2,3 ... n_g；

Step（13）：Using step（11）In raw data matrix X and equation below calculate class between mean dispersion error matrix S_b：

$S_b=\underset{g=1}{\overset{c}{\mathrm{\Σ}}}{({\stackrel{\→}{d}}_x^g-{\stackrel{\→}{d}}_x)}^T\·({\stackrel{\→}{d}}_x^g-{\stackrel{\→}{d}}_x)$

Wherein,It is defined as the mean vector of all samples,It is defined as the mean vector of g class sample；

Step（14）, using step（12）And step（13）In S_w、S_bAnd formulaCalculate eigenvalue λ₁, λ₂,…,λ_c-1And the characteristic vector corresponding to eigenvalueAnd obtain projection matrix $W_{\mathrm{LDA}}=[{\stackrel{\→}{e}}_1^T,{\stackrel{\→}{e}}_2^T,\·\·\·{\stackrel{\→}{e}}_{c-1}^T];$

Step（15）：To step（14）In projection matrix W_LDACarry out PCA dimension-reduction treatment, obtain PCA projection matrix W_PCA, Again by PCA projection matrix W_PCAProject in q dimension space, obtain q dimension space eigenmatrix X_PCA, wherein, X_PCA=X·W_PCA；

Step（16）：By W_LDA、W_PCAAnd X_PCAComplete final feature extraction using equation below：

$\∂=X_{\mathrm{PCA}}\·W_{\mathrm{LDA}}=X\·W_{\mathrm{PCA}}\·W_{\mathrm{LDA}}$

Then after the individual not projection of cospectral graph of m, eigenmatrix is respectivelyWherein,It is defined as the spy after projecting Levy matrix；

Step（17）：Using formulaAfter the different collection of illustrative plates projections of i-th sample Eigenmatrix carries out the multispectral fusion feature vector that fusion treatment obtains i-th sample, and all of sample is carried out same Fusion treatment, obtains the multispectral fusion feature matrix of all samplesWherein,Eigenmatrix vector after definition projection, is θ_f It is defined as the combination coefficient of f kind collection of illustrative plates, f=1,2,3 ... m.

A kind of optimization method as the present invention：Described step（2）Including specifically processing as follows：

Step（21）：By step（17）In the multispectral fusion feature matrix that obtainsSubstitute into such as minor function：

$a_z^{*}=\max (\underset{z=1}{\overset{n}{\mathrm{\Σ}}}{a}_z-\underset{z=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{a}_z\·a_j\·l_z\·l_j\·k({\stackrel{\→}{\mathrm{\α}}}_z,{\stackrel{\→}{\mathrm{\α}}}_j)),s.t.\underset{z=1}{\overset{n}{\mathrm{\Σ}}}{a}_z\·l_z=0,a_z\≥0,$ Try to achieve $a_z^{*}>0$ When supporting vectorWherein, z=1,2,3 ... n, j=1,2,3 ... n,It is defined as the optimization function of the multispectral fusion feature vector of z-th sample；

Step（22）：Using step（21）The supporting vector obtainingTry to achieve the multispectral fusion of z-th sample with equation below Bigoted amount b of characteristic vector^* _z：

${b^{*}}_z=l_z-\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{l}_j\·a_j^{*}\·k({\stackrel{\→}{\mathrm{\α}}}_z,{\stackrel{\→}{\mathrm{\α}}}_j);$

Step（23）：Step（22）Bigoted amount b obtaining^* _zAnd supporting vectorSubstitute into as in minor function：

$f\left({\stackrel{\→}{\mathrm{\α}}}_z\right)=\mathrm{sgn}(\underset{z=1}{\overset{n}{\mathrm{\Σ}}}{l}_z\·a_z^{*}\·k({\stackrel{\→}{\mathrm{\α}}}_z^{*},\stackrel{\→}{\mathrm{\α}})+{b^{*}}_z),$ Wherein, k () is defined as the kernel operation of support vector machine,I.e. Discriminant function for SVM classifier.

The present invention compared with prior art has the advantage that：

Dissimilar spectral data can be carried out multidimensional characteristic fusion by the present invention, can be efficiently applied to divide based on spectrogram Analysis complex mixture Classification and Identification.

Brief description

Fig. 1 is many spectrograms Feature fusion flow chart in the present invention.

Specific embodiment

The present invention is described in further detail below in conjunction with the accompanying drawings：

The present invention devises a kind of many spectrograms Feature Fusion recognition methodss based on PCA_LDA analysis, including concrete as follows Step：

Step（1）：N sample of collection, sets n sample and belongs to c kind classification, and each sample is chosen with m different spectrum Figure, using PCA_LDA method extract all samples chromatogram characteristic, and by extract all samples chromatogram characteristic be fused to many Spectrum fusion feature matrix；

Step（2）：Using step（1）In multispectral fusion feature matrix set up multispectral fusion SVM classifier；

Step（3）：Using step（2）The multispectral fusion SVM classifier of middle foundation is to step（1）The sample of middle collection is carried out Identification.

As shown in figure 1, a kind of optimization method as the present invention：Described step（1）Including specifically processing as follows：

Step（11）：The training sample set data of i-th sample of labelling isThe m dimension data collection of i-th sample to Measure and beThen n × m raw data matrix of all samples isWherein, i=1, 2,3 ... n, l_iIt is defined asClass label；

Step（12）：Using step（11）In raw data matrix X and equation below calculate class in mean dispersion error matrix S_w：

$S_w=\underset{g=1}{\overset{c}{\mathrm{\Σ}}}\underset{p=1}{\overset{n_g}{\mathrm{\Σ}}}{({\stackrel{\→}{x}}_p^g-{\stackrel{\→}{t}}_x^g)}^T\·({\stackrel{\→}{x}}_p^g-{\stackrel{\→}{t}}_x^g)$

Wherein, n_gRepresent the number of samples of g class,It is defined as the mean vector of the sample of g class, g=1,2,3 ... c,It is defined as the vector of p-th sample in g class sample, T is defined as matrix transpose, p=1,2,3 ... n_g；

Step（13）：Using step（11）In raw data matrix X and equation below calculate class between mean dispersion error matrix S_b：

$S_b=\underset{g=1}{\overset{c}{\mathrm{\Σ}}}{({\stackrel{\→}{d}}_x^g-{\stackrel{\→}{d}}_x)}^T\·({\stackrel{\→}{d}}_x^g-{\stackrel{\→}{d}}_x)$

Wherein,It is defined as the mean vector of all samples,It is defined as the mean vector of g class sample；

Step（14）, using step（12）And step（13）In S_w、S_bAnd formulaCalculate eigenvalue λ₁, λ₂,…,λ_c-1And the characteristic vector corresponding to eigenvalueAnd obtain projection matrix $W_{\mathrm{LDA}}=[{\stackrel{\→}{e}}_1^T,{\stackrel{\→}{e}}_2^T,\·\·\·{\stackrel{\→}{e}}_{c-1}^T];$

Step（15）：To step（14）In projection matrix W_LDACarry out PCA dimension-reduction treatment, obtain PCA projection matrix W_PCA, Again by PCA projection matrix W_PCAProject in q dimension space, obtain q dimension space eigenmatrix X_PCA, wherein, X_PCA=X·W_PCA；

Step（16）：By W_LDA、W_PCAAnd X_PCAComplete final feature extraction using equation below：

$\∂=X_{\mathrm{PCA}}\·W_{\mathrm{LDA}}=X\·W_{\mathrm{PCA}}\·W_{\mathrm{LDA}}$

Then after the individual not projection of cospectral graph of m, eigenmatrix is respectivelyWherein,It is defined as the spy after projecting Levy matrix；

Step（17）：Using formulaAfter the different collection of illustrative plates projections of i-th sample Eigenmatrix carries out the multispectral fusion feature vector that fusion treatment obtains i-th sample, and all of sample is carried out same Fusion treatment, obtains the multispectral fusion feature matrix of all samplesWherein,Eigenmatrix vector after definition projection, is θ_f It is defined as the combination coefficient of f kind collection of illustrative plates, f=1,2,3 ... m.

A kind of optimization method as the present invention：Described step（2）Including specifically processing as follows：

Step（21）：By step（17）In the multispectral fusion feature matrix that obtainsSubstitute into such as minor function：

$a_z^{*}=\max (\underset{z=1}{\overset{n}{\mathrm{\Σ}}}{a}_z-\underset{z=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{a}_z\·a_j\·l_z\·l_j\·k({\stackrel{\→}{\mathrm{\α}}}_z,{\stackrel{\→}{\mathrm{\α}}}_j)),s.t.\underset{z=1}{\overset{n}{\mathrm{\Σ}}}{a}_z\·l_z=0,a_z\≥0,$ Try to achieve $a_z^{*}>0$ When supporting vectorWherein, z=1,2,3 ... n, j=1,2,3 ... n,It is defined as the optimization function of the multispectral fusion feature vector of z-th sample；

Step（22）：Using step（21）The supporting vector obtainingTry to achieve the multispectral fusion of z-th sample with equation below Bigoted amount b of characteristic vector^* _z：

${b^{*}}_z=l_z-\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{l}_j\·a_j^{*}\·k({\stackrel{\→}{\mathrm{\α}}}_z,{\stackrel{\→}{\mathrm{\α}}}_j);$

Step（23）：Step（22）Bigoted amount b obtaining^* _zAnd supporting vectorSubstitute into as in minor function：

$f\left({\stackrel{\→}{\mathrm{\α}}}_z\right)=\mathrm{sgn}(\underset{z=1}{\overset{n}{\mathrm{\Σ}}}{l}_z\·a_z^{*}\·k({\stackrel{\→}{\mathrm{\α}}}_z^{*},\stackrel{\→}{\mathrm{\α}})+{b^{*}}_z),$ Wherein, k () is defined as the kernel operation of support vector machine,I.e. Discriminant function for SVM classifier.

In a particular embodiment, our experiment respectively the indigo plant wine sample to 50 skies and 50 seas indigo plant wine sample collection Raman Spectrogram, mass spectrum and ion transfer spectrogram.

Raman spectrogram collection experiment is as follows：

Draw wine sample with capillary tube, be added to injection port, carry out spectrogram collection under conditions of HONGGUANG 632.8nm, collection During indoor holding dark state, in order to avoid the impact to experiment for the visible ray.

Mass spectrum collection experiment is as follows：

It is analyzed using the direct Head-space sampling of atmospheric pressure capillary tube under room temperature.Major parameter condition：1）Ionization mode：Single Photon ionizes；2）Ionized region stable gas pressure is in about 15.50Pa；3）Accelerating region voltage is 2650V, and 250 micron capillary column directly enter Sample, no heating measures；4）Every TOF full Spectral Signal cumulative time is 15s；5）Head space volume about 10ml.

Test sample collection assumes extraordinary separation property, the blue sample in the indigo plant sample in sky and sea in the feature space after fusion This is assembled in three dimensions in two different regions in feature space, illustrates that PCA_LDA feature proposed by the present invention carries Take with many spectrograms Feature Fusion Algorithm to extract different brackets Chinese liquor internal characteristicses be effective.

Claims (1)

1. a kind of many spectrograms Feature Fusion recognition methodss based on PCA_LDA analysis are it is characterised in that include specifically walking as follows Suddenly：

Step (1)：N sample of collection, sets n sample and belongs to c kind classification, and each sample is chosen with m not cospectral graph, profit Extract the chromatogram characteristic of all samples with PCA_LDA method, and by extract the chromatogram characteristic of all samples is fused to multispectral melting Close eigenmatrix；

Described step (1) includes specifically processing as follows：

Step (11)：The training sample set data of i-th sample of labelling isThe m dimension data collection vector of i-th sample isThen n × m raw data matrix of all samples isWherein, i=1,2, 3 ... n, l_iIt is defined asClass label；

Step (12)：Calculate mean dispersion error matrix S in class using the raw data matrix X in step (11) and equation below_w：

$S_w=\underset{g=1}{\overset{c}{\Σ}}\underset{p=1}{\overset{n_g}{\Σ}}{({\stackrel{\→}{x}}_p^g-{\stackrel{\→}{t}}_x^g)}^T\·({\stackrel{\→}{x}}_p^g-{\stackrel{\→}{t}}_x^g)$

Wherein, n_gRepresent the number of samples of g class,It is defined as the mean vector of the sample of g class, g=1,2,3 ... c,Fixed Justice is defined as matrix transpose, p=1,2,3 ... n for the vector of p-th sample in g class sample, T_g；

Step (13)：Calculate mean dispersion error matrix S between class using the raw data matrix X in step (11) and equation below_b：

$S_b=\underset{g=1}{\overset{c}{\Σ}}{({\stackrel{\→}{d}}_x^g-{\stackrel{\→}{d}}_x)}^T\·({\stackrel{\→}{d}}_x^g-{\stackrel{\→}{d}}_x)$

Wherein,It is defined as the mean vector of all samples,It is defined as the mean vector of the sample of g class；

Step (14)：Using the S in step (12) and step (13)_w、S_bAnd formulaCalculate eigenvalue λ₁, λ₂..., λ_c-1 And the characteristic vector corresponding to eigenvalueAnd obtain projection matrix

Step (15)：To the projection matrix W in step (14)_LDACarry out PCA dimension-reduction treatment, obtain PCA projection matrix W_PCA, then will PCA projection matrix W_PCAProject in q dimension space, obtain q dimension space eigenmatrix X_PCA, wherein, X_PCA=X W_PCA；

Step (16)：By W_LDA、W_PCAAnd X_PCAComplete final feature extraction using equation below：

$\∂=X_{PCA}\·W_{LDA}=X\·W_{PCA}\·W_{LDA}$

Then after the individual not projection of cospectral graph of m, eigenmatrix is respectivelyWherein,It is defined as the feature square after projecting Battle array；

Step (17)：Using formulaBy feature after the different collection of illustrative plates projections of i-th sample Matrix carries out the multispectral fusion feature vector that fusion treatment obtains i-th sample, and carries out same fusion to all of sample Process, obtain the multispectral fusion feature matrix of all samplesWherein,Eigenmatrix vector after definition projection, is θ_fDefinition For the combination coefficient of f kind collection of illustrative plates, f=1,2,3 ... m；

Step (2)：Set up multispectral fusion SVM classifier using the multispectral fusion feature matrix in step (1)；

Described step (2) includes specifically processing as follows：

Step (21)：The multispectral fusion feature matrix that will obtain in step (17)Substitute into such as minor function：

Try to achieveWhen support VectorWherein, z=1,2,3 ... n, j=1,2,3 ... n,It is defined as the optimization of the multispectral fusion feature vector of z-th sample Function；a_zAnd a_jIt is all Lagrange multiplier, wherein z, j corresponds to multiplier subscript, and value is from 1 to n；l_zRepresent the classification mark of z sample Note, value from 1 to c, l_jRepresent the category label of j sample, value is from 1 to c；

Step (22)：The supporting vector being obtained using step (21)Try to achieve z-th sample multispectral fusion feature arrow with equation below Bigoted amount b of amount^* _z：

${b^{*}}_z=l_z-\underset{j=1}{\overset{n}{\Σ}}{l}_j\·a_j^{*}\·k({\stackrel{\→}{\mathrm{\α}}}_z,{\stackrel{\→}{\mathrm{\α}}}_j)$

Step (23)：Bigoted amount b that step (22) obtains^* _zAnd supporting vectorSubstitute into as in minor function：

Wherein, k () is defined as the kernel operation of support vector machine,I.e. Discriminant function for SVM classifier；

Step (3)：Using the multispectral fusion SVM classifier set up in step (2), the sample of collection in step (1) is known Not.