CN107192686A - A kind of Possibility Fuzzy Clustering local tea variety discrimination method of fuzzy covariance matrix - Google Patents
A kind of Possibility Fuzzy Clustering local tea variety discrimination method of fuzzy covariance matrix Download PDFInfo
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Abstract
The invention discloses a kind of Possibility Fuzzy Clustering local tea variety discrimination method of fuzzy covariance matrix, comprise the following steps：First, the tealeaves sample of several kinds is collected, the infrared spectrum information that diffuses of tealeaves sample is obtained with infrared spectrometer；2nd, tealeaves sample infrared spectrum is pre-processed with multiplicative scatter correction MSC；3rd, the tealeaves sample ir data obtained in step 2 is subjected to dimensionality reduction compression using principal component analysis PCA；4th, by the infrared spectrum compressed data obtained in step 3 with obtained after linear discriminant analysis LDA Extraction and discrimination information comprising authentication information training sample and test sample data；5th, in step 4 comprising authentication information test sample with a kind of Possibility Fuzzy Clustering method of fuzzy covariance matrix with the local tea variety in differential test sample.The present invention has the advantages that detection speed is fast, differentiates accuracy rate height, green non-pollution, required tealeaves sample is few, can quickly realize local tea variety discriminating.
Description
Technical field
The present invention relates to a kind of local tea variety mirror method for distinguishing, and in particular to a kind of possibility of fuzzy covariance matrix is obscured
Cluster local tea variety discrimination method.
Background technology
Middle infrared spectrum detection technique is used as a kind of Fast nondestructive evaluation technology, the in recent years detection and analysis applied to food
In.Mid-infrared spectral wave-number range is in 4000cm-1~400cm-1Between, most inorganic compound and organic compound
Chemical bond oscillations fundamental frequency in this region.The three-dimensional knot of functional group, the classification of compound and compound in different molecules
Structure, its infrared absorption spectroscopy is not quite similar.Mid-infrared light spectral technology with it easily and fast, it is efficient, lossless, inexpensive the features such as
Effective detection technology as detection food and medicine.
The purpose of cluster is that according to certain similarity criterion data set is divided into several subsets.Will be big by clustering method
Batch data is categorized as the cluster of many essential connections.Common clustering method has two kinds：Hard cluster and soft (fuzzy) clustering method.Before
Person is often applied to the obvious situation of cluster boundary；It is not that the system being apparent from uses fuzzy clustering method then for cluster boundary
It is more particularly suitable.
Possibility Fuzzy C-Means Clustering (PFCM) must first run Fuzzy C-Means Clustering (FCM) and carry out calculating parameter, increase
Cluster operation time is added.(Wu little Hong, Zhou Jianjiang wait may to new possibility Fuzzy C-Means Clustering (NPFCM) clustering method
Property Fuzzy C-Means Clustering new algorithm [J] electronic letters, vols, 2008.10:1996~the problem of 2000) solve PFCM, reduce
Cluster operation time improves the degree of accuracy simultaneously.But NPFCM clustering methods make in the data of the irregular cluster shape of processing
It is that Euclidean distance is calculated, clusters the scrambling of accuracy rate meeting factor data distribution and be greatly affected so that be poly-
There is certain error in class result.
After the mid-infrared light modal data of infrared spectrometer detection collection tealeaves in use, easily occur during to cluster data
Irregular border is presented in data set after cluster, because NPFCM clustering methods are irregular to distribution shape using Euclidean distance
Data set processing ability it is unsatisfactory, thus handle the type tealeaves mid-infrared light modal data when easily drop accuracy rate
It is low.The present invention improved and optimized on the basis of NPFCM clustering methods, it is proposed that a kind of fuzzy covariance matrix can
Can fuzzy clustering method to realize the Variety identification of tealeaves.A kind of Possibility Fuzzy Clustering method of fuzzy covariance matrix is being calculated
Local auto-adaptive distance measure is employed during cluster and instead of Euclidean distance, accuracy rate but also the reduction of cluster is not only increased
Cluster operation time.
The content of the invention
It can be deposited in clustering distribution tealeaves ir data in irregular shape the present invention be directed to NPFCM clustering methods
In the defect of necessarily cluster error, a kind of infrared spectrum tealeaves product of the Possibility Fuzzy Clustering method of fuzzy covariance matrix are proposed
Plant discrimination method.Compared to original NPFCM clustering methods, a kind of Possibility Fuzzy Clustering side of fuzzy covariance matrix of the invention
Method replaces Euclidean distance using local auto-adaptive distance measure, and adaptive distance measure can be by estimating that fuzzy covariance matrix is adjusted
Whole distance measure, so as to realize accurate cluster different shape cluster data, can fast and effectively cluster the ir data of tealeaves,
The accuracy rate differentiated to local tea variety can be improved simultaneously.Fast, the green non-pollution with detection speed, required tealeaves sample is few etc.
Advantage.
The principle of foundation of the present invention：Research shows that the infrared diffusing reflection spectrum of tealeaves contains the component letter inside tealeaves
Breath, the infrared diffusing reflection spectrum corresponding to different cultivars tealeaves is different.The infrared light of tealeaves is compressed with principal component analysis (PCA)
Modal data, the authentication information of infrared spectrum is extracted using linear discriminant analysis (LDA), finally with a kind of fuzzy covariance matrix
Possibility Fuzzy Clustering method differentiates local tea variety.Concrete technical scheme is described as follows：
A kind of Possibility Fuzzy Clustering local tea variety discrimination method of fuzzy covariance matrix, comprises the following steps：
Step 1: tealeaves sample infrared spectrum is gathered：The tealeaves sample of several kinds is collected, is obtained with infrared spectrometer
The infrared spectrum information that diffuses of tealeaves sample；Tealeaves sample is divided into training sample and test sample；Classification number c, training are set
Sample number nrWith test sample number n；
Step 2: being pre-processed to tealeaves sample infrared spectrum：Tealeaves sample infrared spectrum is entered with multiplicative scatter correction MSC
Row pretreatment；
Step 3: carrying out dimension-reduction treatment to tealeaves sample infrared spectrum：It will be obtained using principal component analysis PCA in step 2
Tealeaves sample ir data be compressed；
Step 4: by the tealeaves sample infrared spectrum compressed data linear discriminant analysis LDA obtained in above-mentioned steps three
Training sample and test sample data comprising authentication information are obtained after Extraction and discrimination information；
Step 5: fuzzy with a kind of possibility of fuzzy covariance matrix to the test sample comprising authentication information in step 4
Clustering method is with the local tea variety in differential test sample.
Further, the spectrum wave-number range of the infrared spectrum information that diffuses is 4001.569cm-1~401.1211cm-1, the spectroscopic data of collection tealeaves sample is the data of 1868 dimensions.
Further, step one also includes：Indoor temperature is kept in the infrared diffusing reflection spectrum information process for gathering tealeaves
It is basically identical with humidity.
Further, c=3.
Further, the detailed process of step 5 includes as follows：
(1) initialize：Weighted index m and p value are set, and meet m0 (1 ,+∞), p ∈ (1 ,+∞)；D is test sample
Dimension；It is r to set iterations initial value r=0 and maximum iterationmax；It is ε to set iteration worst error parameter；To surveying
Sample this operation fuzzy C-means clustering FCM, FCM run abort after fuzzy membership and class center it is fuzzy respectively as one kind
The initial fuzzy membership and initial cluster center of the Possibility Fuzzy Clustering method of covariance matrix；
(2) calculate r (r=1,2 ..., rmax) secondary iteration when fuzzy covariance matrix Sfi,r：
In above formula, xkFor k-th of tealeaves examination of infrared spectrum sample, vi,r-1During for the r-1 times iteration in the class of the i-th class
The heart (i=1,2,3), uik,r-1Sample x during for the r-1 times iterationkBelong to the fuzzy membership of the i-th class, Sfi,rIt is the r times iteration
When the i-th class fuzzy covariance matrix；
(3) fuzzy membership angle value u during the r times iteration is calculatedik,r:
In above formulaSample x during for the r-1 times iterationkTo class center vi,r-1Distance,For the r-1 times
Sample x during iterationkTo class center vj,r-1Apart from norm (j=1,2,3)；
In above formula, Ai,rThe norm matrix at ith cluster center when being the r times iteration；Aj,rJth during the r times iteration
The norm matrix of individual cluster centre；D is the dimension of test sample；vj,r-1JLei Lei centers (j=during for the r-1 times iteration
1,2,3)；
(4) representative value t during the r times iteration is calculatedik,r：
tik,rK-th of test sample is under the jurisdiction of the representative value of the i-th class during for the r times iteration；
(5) the i-th Lei Lei centers ν during the r times iteration is calculatedi,r：
(6) when (| | νi,r-νi,r-1||<ε) or (r>rmax) when, then calculate terminate, otherwise from " (2) calculate r (r=1,
2,…,rmax) secondary iteration when fuzzy covariance matrix Sfi,r" restart to calculate；νi,rThe i-th class during for the r times iteration
Class central value, νi,r-1The class central value of the i-th class during for the r-1 times iteration；After iteration ends, according to fuzzy membership angle value and
Class central value determines local tea variety.
Beneficial effects of the present invention：
1st, compared with NPFCM clustering algorithms, a kind of Possibility Fuzzy Clustering algorithm of fuzzy covariance matrix of the invention
Local auto-adaptive distance measure is employed, the data set that NPFCM is randomly distributed shape using Euclidean distance in processing is solved
When there is wrong clustering problem, improve the accuracy rate known clearly to tealeaves data clusters.
2nd, detection speed of the present invention is fast, differentiates that accuracy rate is high, green non-pollution, required tealeaves sample is few, can quickly realize
The discriminating of local tea variety
Brief description of the drawings
Fig. 1 is the flow chart of the present invention；
Fig. 2 is the infrared spectrogram of tealeaves；
Wherein：(a) it is certified products green bamboo snake；(b) it is green bamboo snake inferior；(c) it is Mount Emei Mao Feng；
Fig. 3 is the tealeaves infrared spectrogram after MSC processing；
Fig. 4 is the test sample datagram that is obtained after LDA Extraction and discrimination information of infrared spectrum of tealeaves；
Fig. 5 is a kind of fuzzy membership of the Possibility Fuzzy Clustering method generation of fuzzy covariance matrix.
Embodiment
Below in conjunction with the accompanying drawings and embodiment the invention will be further described.
As shown in figure 1, the inventive method comprises the following steps：
Step 1: tealeaves sample infrared spectrum is gathered：The tealeaves sample of multiple kinds is collected, tea is obtained with infrared spectrometer
The infrared spectrum information that diffuses of leaf sample, spectral information is stored in computer.Kept in experimentation indoor temperature and
Humidity is basically identical；The spectrum wave-number range of the infrared spectrum information that diffuses is 4001.569cm-1~401.1211cm-1, collection
To each tealeaves sample spectrum be 1868 dimensions data.Tealeaves sample is divided into training sample and test sample.Classification is set
Number c (c=3), number of training is nrIt is n with test sample number.
Step 2: being pre-processed to tealeaves sample infrared spectrum：With multiplicative scatter correction (MSC) to tealeaves sample infrared spectrum
Pre-processed.
Step 3: carrying out dimension-reduction treatment to tealeaves sample infrared spectrum：It will be obtained using principal component analysis (PCA) in step 2
The tealeaves sample ir data obtained is compressed.
Step 4: by the tealeaves sample infrared spectrum compressed data linear discriminant analysis obtained in above-mentioned steps three
(LDA) training sample and test sample data comprising authentication information are obtained after Extraction and discrimination information.
Step 5: fuzzy with a kind of possibility of fuzzy covariance matrix to the test sample comprising authentication information in step 4
Clustering method is with the local tea variety in differential test sample.Detailed process is as follows：
(1) initialize：Weighted index m and p value are set, and meet m ∈ (1 ,+∞), p ∈ (1 ,+∞)；D is test specimens
This dimension；It is r to set iterations initial value r=0 and maximum iterationmax；It is ε to set iteration worst error parameter.It is right
Test sample operation fuzzy C-means clustering (FCM), FCM run abort after fuzzy membership and class center respectively as one kind
The initial fuzzy membership and initial cluster center of the Possibility Fuzzy Clustering method of fuzzy covariance matrix；
(2) calculate r (r=1,2 ..., rmax) secondary iteration when fuzzy covariance matrix Sfi,r：
In above formula, xkFor k-th of tealeaves examination of infrared spectrum sample, vi,r-1During for the r-1 times iteration in the class of the i-th class
The heart (i=1,2,3), uik,r-1Sample x during for the r-1 times iterationkBelong to the fuzzy membership of the i-th class, Sfi,rIt is the r times iteration
When the i-th class fuzzy covariance matrix.
(3) fuzzy membership angle value u during the r times iteration is calculatedik,r:
In above formulaSample x during for the r-1 times iterationkTo class center vi,r-1Distance,For the r-1 times
Sample x during iterationkTo class center vj,r-1Apart from norm (j=1,2,3).
In above formula, Ai,rThe norm matrix at ith cluster center when being the r times iteration；Aj,rJth during the r times iteration
The norm matrix of individual cluster centre；D is the dimension of test sample；vj,r-1JLei Lei centers (j=during for the r-1 times iteration
1,2,3)。
(4) representative value t during the r times iteration is calculatedik,r：
tik,rK-th of test sample is under the jurisdiction of the representative value of the i-th class during for the r times iteration.
(5) the i-th Lei Lei centers ν during the r times iteration is calculatedi,r：
(6) when (| | νi,r-νi,r-1||<ε) or (r>rmax) when, then calculate terminate, otherwise from " (2) calculate r (r=1,
2,…,rmax) secondary iteration when fuzzy covariance matrix Sfi,r" restart to calculate.νi,rThe i-th class during for the r times iteration
Class central value, νi,r-1The class central value of the i-th class during for the r-1 times iteration.After iteration ends, according to fuzzy membership angle value and
Class central value determines local tea variety.
With reference to example and accompanying drawing, the present invention is described in more detail.
A kind of infrared spectrum local tea variety discrimination method of the Possibility Fuzzy Clustering of fuzzy covariance matrix of the present invention is fitted
For the discriminating to local tea variety.For example：The discriminating of the local tea varieties such as high-quality green tea, green bamboo snake, Dragon Well tea, Iron Guanyin.Because different product
Tealeaves is planted, its internal composition is different, therefore diffusion infrared spectrum is also different, to realize that the discriminating of local tea variety provides bar
Part.The implementing procedure figure of the present invention is as shown in Figure 1.For convenience of describing, Mount Emei's tealeaves, Leshan high-quality green bamboo snake and bad are chosen
Matter green bamboo snake is experimental subjects.
Embodiment
Step 1: tealeaves sample infrared spectrum is gathered：FTIR-7600 type FTIR spectrums analyzer is started shooting and preheated
1 hour.Scanning times are 32, the wave number 4001.569cm of spectral scan-1~401.1211cm-1, sweep spacing is
1.928cm-1, resolution ratio is 4cm-1.Three kinds of tealeaves samples, Mount Emei's tealeaves, Leshan high-quality green bamboo snake and green bamboo snake inferior.
Tealeaves is ground to be crushed, then after being filtered with 40 mesh sieves, respectively take 0.5g respectively with KBr 1:100 uniform mixing.Each sample
Originally take mixture 1g to carry out press mold, then scanned 3 times with spectrometer, take the average value of 3 times as sample spectrum data.Gather ring
Border temperature is 25 DEG C or so, and relative humidity is 50% or so, and voltage is 220V.Every kind of tealeaves gathers 32 samples, and 96 are obtained altogether
Individual sample.Each sample is the data of one 1868 dimension.It is test set that tealeaves sample per each kind, which chooses 22, then test specimens
This number n is 66.Remaining 10 samples are training set, then number of training nrFor 30.Test set is tealeaves sample to be identified, instruction
Practice tealeaves sample of the collection for known kind.Classification number c=3 is set.The infrared spectrum of tealeaves sample is as shown in Figure 2.
Step 2: being pre-processed to tealeaves sample infrared spectrum：With multiplicative scatter correction (MSC) to tealeaves sample infrared spectrum
Pre-processed.Pretreated tealeaves infrared spectrogram is as shown in Figure 3.
Step 3: the dimension-reduction treatment of tealeaves sample infrared spectrum：It will be obtained using principal component analysis (PCA) in step 2
Tealeaves sample ir data compression.Because preceding 14 principal components, which add up confidence level, is more than 98%, using principal component
Tealeaves sample infrared spectrum progress feature decomposition is obtained preceding 14 characteristic vectors and 14 characteristic values by analysis method (PCA).Often
Individual characteristic vector is all the data of 1868 dimensions, and characteristic value is specific as follows
λ1=293.91；λ2=129.02；λ3=19.00；λ4=14.88；λ5=6.43；
λ6=3.82；λ7=2.00；λ8=1.43；λ9=1.07；λ10=0.63；
λ11=0.40；λ12=0.32；λ13=0.27；λ14=0.23；
Tealeaves sample infrared spectrum is projected to the data that 14 dimensions are obtained in 14 characteristic vectors, i.e., is compressed to from 1868 dimensions
14 dimensions.
Step 4: by the tealeaves sample infrared spectrum compressed data linear discriminant analysis obtained in above-mentioned steps three
(LDA) training sample and test sample data comprising authentication information are obtained after Extraction and discrimination information.
Discriminant vectorses number is 2, is obtained using after the authentication information of 14 dimension datas in linear discriminant analysis (LDA) extraction step three
To the training sample comprising authentication information and test sample data, wherein test sample data are as shown in Figure 4.
Step 5: using a kind of possibility mould of fuzzy covariance matrix to the test sample comprising authentication information in step 4
Clustering method is pasted with the local tea variety in differential test sample.It is specific as follows：
(1) initialize：Weighted index m and p value are set, and meet m ∈ (1 ,+∞), p ∈ (1 ,+∞)；D is test specimens
This dimension；It is r to set iterations initial value r=0 and maximum iterationmax；Iteration worst error parameter ε is set；To surveying
This operation of sample fuzzy C-means clustering (FCM), FCM run abort after fuzzy membership and class center respectively as a kind of mould
Paste the initial fuzzy membership and initial cluster center of the Possibility Fuzzy Clustering method of covariance matrix；
The numerical value of initialization is set：From step one：Classification number c=3 (i.e. three classifications), test sample number n=66.
Weighted index m=2, p=2, iterations initial value r=0 and greatest iteration number r are setmax=100, error higher limit ε=
0.00001, the dimension d of test sample is 2.Two groups of one-dimensional test datas to step 4 carry out fuzzy C-means clustering (FCM),
FCM run abort after cluster centre as a kind of fuzzy covariance matrix Possibility Fuzzy Clustering method initial cluster center,
Then a kind of initial cluster center of the Possibility Fuzzy Clustering method of fuzzy covariance matrix is：v1,0=(- 0.1580,0.0403),
v2,0=(- 0.0020,0.0049), v3.0=(0.1194, -0.0056)；
(2) calculate r (r=1,2 ..., rmax) secondary iteration when fuzzy covariance matrix Sfi,r：
In above formula, xkFor k-th of tealeaves examination of infrared spectrum sample, vi,r-1During for the r-1 times iteration in the class of the i-th class
The heart (i=1,2,3), uik,r-1Sample x during for the r-1 times iterationkBelong to the fuzzy membership of the i-th class, Sfi,rIt is the r times iteration
When the i-th class fuzzy covariance matrix.
(3) fuzzy membership angle value u during the r times iteration is calculatedik,r:
In above formulaSample x during for the r-1 times iterationkTo class center vi,r-1Distance,For the r-1 times
Sample x during iterationkTo class center vj,r-1Apart from norm (j=1,2,3), vj,r-1During for the r-1 times iteration in the class of jth class
The heart (j=1,2,3).
In above formula, Ai,rThe norm matrix at ith cluster center when being the r times iteration；D is the dimension of test sample.
(4) representative value t during the r times iteration is calculatedik,r：
tik,rK-th of test sample is under the jurisdiction of the representative value of the i-th class during for the r times iteration.
(5) the i-th Lei Lei centers ν during the r times iteration is calculatedi,r：
(6) when (| | νi,r-νi,r-1||<ε) or (r>rmax) when, then calculate terminate, otherwise from " (2) calculate r (r=1,
2,…,rmax) secondary iteration when fuzzy covariance matrix Sfi,r" restart to calculate.νi,rThe i-th class during for the r times iteration
Class central value, νi,r-1The class central value of the i-th class during for the r-1 times iteration.
Experimental result：R=64 during iteration ends, vi,64For：v1,64=(- 0.1645,0.0302)；v2,64=(0.0031,
0.0051)；v3,64=(0.1245,0.0032)；Fuzzy membership u during iteration endsik,64As shown in Figure 5.According to fuzzy membership
Degree can obtain the discriminating rate of accuracy reached 94% of test sample.
Those listed above is a series of to be described in detail only for feasibility embodiment of the invention specifically
Bright, they simultaneously are not used to limit the scope of the invention, all equivalent implementations made without departing from skill spirit of the present invention
Or change should be included in the scope of the protection.
Claims (4)
1. the Possibility Fuzzy Clustering local tea variety discrimination method of a kind of fuzzy covariance matrix, it is characterised in that including following step
Suddenly：
Step 1: tealeaves sample infrared spectrum is gathered：The tealeaves sample of several kinds is collected, tealeaves is obtained with infrared spectrometer
The infrared spectrum information that diffuses of sample；Tealeaves sample is divided into training sample and test sample；Classification number c, training sample are set
Number nrWith test sample number n；
Step 2: being pre-processed to tealeaves sample infrared spectrum：Tealeaves sample infrared spectrum is carried out in advance with multiplicative scatter correction MSC
Processing；
Step 3: carrying out dimension-reduction treatment to tealeaves sample infrared spectrum：Using principal component analysis PCA by the tea obtained in step 2
Leaf sample ir data is compressed；
Step 4: the tealeaves sample infrared spectrum compressed data linear discriminant analysis LDA obtained in above-mentioned steps three is extracted
Training sample and test sample data comprising authentication information are obtained after authentication information；
Step 5: to the test sample comprising authentication information in step 4 with a kind of Possibility Fuzzy Clustering of fuzzy covariance matrix
Method is with the local tea variety in differential test sample.
2. a kind of Possibility Fuzzy Clustering local tea variety discrimination method of fuzzy covariance matrix according to claim 1, its
It is characterised by, the spectrum wave-number range of the infrared spectrum information that diffuses is 4001.569cm-1~401.1211cm-1, collection
The spectroscopic data of tealeaves sample is the data of 1868 dimensions.
3. a kind of Possibility Fuzzy Clustering local tea variety discrimination method of fuzzy covariance matrix according to claim 1, its
It is characterised by, step one also includes：Indoor temperature and humidity is kept in the infrared diffusing reflection spectrum information process for gathering tealeaves
It is basically identical.
4. a kind of Possibility Fuzzy Clustering local tea variety discrimination method of fuzzy covariance matrix according to claim 1, its
It is characterised by, the detailed process of step 5 is including as follows：
(1) initialize：Weighted index m and p value are set, and meet m ∈ (1 ,+∞), p ∈ (1 ,+∞)；D is test sample
Dimension；It is r to set iterations initial value r=0 and maximum iterationmax；It is ε to set iteration worst error parameter；To test
Sample operation fuzzy C-means clustering FCM, FCM run abort after fuzzy membership and class center respectively as the fuzzy association of one kind
The initial fuzzy membership and initial cluster center of the Possibility Fuzzy Clustering method of variance matrix；
(2) calculate r (r=1,2 ..., rmax) secondary iteration when fuzzy covariance matrix Sfi,r：
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mi>f</mi>
<mi>i</mi>
<mo>,</mo>
<mi>r</mi>
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</msub>
<mo>=</mo>
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<mi>&Sigma;</mi>
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<msup>
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<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</msubsup>
</mrow>
</mfrac>
</mrow>
In above formula, xkFor k-th of tealeaves examination of infrared spectrum sample, vi,r-1I-th Lei Lei centers (i during for the r-1 times iteration
=1,2,3), uik,r-1Sample x during for the r-1 times iterationkBelong to the fuzzy membership of the i-th class, Sfi,rI-th when being the r times iteration
The fuzzy covariance matrix of class；
(3) fuzzy membership angle value u during the r times iteration is calculatedik,r:
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>i</mi>
<mi>k</mi>
<mo>,</mo>
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<mo>=</mo>
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<mo>&Sigma;</mo>
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<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>c</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<msubsup>
<mi>D</mi>
<mrow>
<msub>
<mi>ikA</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<mi>r</mi>
<mo>-</mo>
<mn>1</mn>
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<mn>2</mn>
</msubsup>
<msubsup>
<mi>D</mi>
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<mi>j</mi>
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<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mfrac>
</msup>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>,</mo>
<mo>&ForAll;</mo>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
1
In above formulaSample x during for the r-1 times iterationkTo class center vi,r-1Distance,For the r-1 times iteration
When sample xkTo class center vj,r-1Apart from norm (j=1,2,3)；
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<mi>D</mi>
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<mi>jkA</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
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<mo>-</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
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<mo>(</mo>
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</msub>
<mo>-</mo>
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</mrow>
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<mo>)</mo>
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<mi>f</mi>
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</msub>
<msup>
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<mn>1</mn>
<mi>d</mi>
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</msup>
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<mo>)</mo>
</mrow>
</mrow>
In above formula, Ai,rThe norm matrix at ith cluster center when being the r times iteration；Aj,rJ-th during the r times iteration is poly-
The norm matrix at class center；D is the dimension of test sample；vj,r-1JLei Lei centers during for the r-1 times iteration (j=1,2,
3)；
(4) representative value t during the r times iteration is calculatedik,r：
<mrow>
<msub>
<mi>t</mi>
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<mo>,</mo>
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</mrow>
<mn>2</mn>
</msubsup>
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<mi>f</mi>
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</mrow>
</msub>
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<mn>1</mn>
<mi>d</mi>
</mfrac>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mfrac>
<mn>1</mn>
<mrow>
<mi>p</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mfrac>
</msup>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>,</mo>
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<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
tik,rK-th of test sample is under the jurisdiction of the representative value of the i-th class during for the r times iteration；
(5) the i-th Lei Lei centers ν during the r times iteration is calculatedi,r：
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
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</mrow>
</msub>
<mo>=</mo>
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<mo>&Sigma;</mo>
<mrow>
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<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mrow>
<mo>(</mo>
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<mi>u</mi>
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</mrow>
<mi>m</mi>
</msubsup>
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<mi>t</mi>
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</mrow>
<mi>p</mi>
</msubsup>
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</mrow>
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</munderover>
<mrow>
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<mi>u</mi>
<mrow>
<mi>i</mi>
<mi>k</mi>
<mo>,</mo>
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</mrow>
<mi>m</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>t</mi>
<mrow>
<mi>i</mi>
<mi>k</mi>
<mo>,</mo>
<mi>r</mi>
</mrow>
<mi>p</mi>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>,</mo>
<mo>&ForAll;</mo>
<mi>i</mi>
</mrow>
(6) when (| | νi,r-νi,r-1||<ε) or (r>rmax) when, then calculate terminate, otherwise from " (2) calculate r (r=1,
2,…,rmax) secondary iteration when fuzzy covariance matrix Sfi,r" restart to calculate；νi,rThe i-th class during for the r times iteration
Class central value, νi,r-1The class central value of the i-th class during for the r-1 times iteration；After iteration ends, according to fuzzy membership angle value and
Class central value determines local tea variety.
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| CN107886115A (en) * | 2017-10-27 | 2018-04-06 | 江苏大学 | A kind of tealeaves mid-infrared light profile classification method of adaptively possible C mean clusters |
| CN108920428A (en) * | 2018-06-07 | 2018-11-30 | 辽宁工程技术大学 | A kind of fuzzy distance method of discrimination based on joint Fuzzy Extension Principle |
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