Spectral Classification Using Fuzzy Hyperbolic Cosine Discriminant Analysis
WU Bin1, 2*, LIU Fu-bei3, WU Xiao-hong3
1. School of Information Engineering, Chuzhou Polytechnic, Chuzhou 239000, China
2. School of Computer Science and Engineering, Southeast University, Nanjing 211102, China
3. School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China
Abstract：Traditional linear discriminant analysis (LDA) has a small sample problem when directly processing high-dimensional spectral data, while hyperbolic cosine discriminant analysis (HCMDA) can solve the small sample problem. To further improve the classification accuracy of HCMDA and process noisy spectral data, a fuzzy hyperbolic cosine discriminant analysis (FHCMDA) algorithm was proposed by combining fuzzy set theory with hyperbolic cosine similarity. Furthermore, a model based on FHCMDA and K-nearest neighbors (KNN) was built to classify meat mid-infrared (MIR) spectra and apple near-infrared (NIR) spectra, respectively, and was compared with HCMDA to contrast their classification accuracies. FHCMDA calculates the fuzzy membership values by using the training samples and their means, the fuzzy intra-class scatter matrix and the fuzzy inter-class scatter matrix, the fuzzy intra-class hyperbolic cosine function and the fuzzy inter-class hyperbolic cosine function, and the eigenvector through feature decomposition. At first, MIR spectra were obtained for three meat variaties (chicken, turkey, and pork) and NIR spectra for four apple varieties (Red Fuji, Huaniu, Huangjiao, and Jiana), with 40 samples for each meat type and 50 for each apple type. Secondly, multivariate scattering correction (MSC) was applied to preprocess the NIR spectral data of apples, eliminating spectral differences caused by varying scattering levels and enhancing their correlation. Thirdly, the initial clustering centers for meat and apple were determined, and the fuzzy membership degree of each sample was calculated. The feature decomposition was completed by HCMDA and FHCMDA, respectively, using the calculated fuzzy hyperbolic cosine function to extract features from spectral data. Finally, KNN was used for classification, and the classification accuracies of HCMDA and FHCMDA were obtained and compared. The final results of this experiment were as follows: HCMDA+KNN achieved classification accuracies of 90.48% for the meat variety and 76.67% for the apple variety. The classification accuracy of FHCMDA+KNN was 97.62% for the meat variety and 91.67% for the apple variety. The above experimental results show that fuzzy hyperbolic cosine discriminant analysis combined with KNN is an effective method for identifying food varieties, with identification accuracy significantly higher than that of HCMDA+KNN.
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