Abstract：To explore the intrinsic structure and the low dimensional representation of high dimensional data and find explicit mapping in some manifold learning algorithms, spherical cover classification algorithm based on manifold dimension reduction space of local and global mapping is proposed. The mapping model combining local information and global information is extracted firstly. The local laplacian matrix and the global laplacian matrix are optimized separately. The low dimensional representation of training data is obtained by eigen-decomposition of the laplacian matrix. Then the low dimensional representation of testing data is obtained by kernel mapping. Finally, the spherical cover classification model in low dimensional space is constructed. Extensive experiments are conducted on MNIST dataset, YaleB face dataset and AR dataset, and the results verify the effectiveness of the proposed algorithm and its value in the application fields.
胡正平，杜立翠，赵淑欢. 基于局部和全局映射函数的流形降维空间球形覆盖分类算法*[J]. 模式识别与人工智能, 2015, 28(4): 354-360.
HU Zheng-Ping, DU Li-Cui, ZHAO Shu-Huan. Spherical Cover Classification Algorithm Based on Manifold Dimension Reduction Space of Local and Global Mapping. , 2015, 28(4): 354-360.
[1] Angiulli F. Prototype-Based Domain Description for One-Class Classification.Trans on Pattern Analysis and Machine Intelligence, 2012, 34(6): 1131-1144 [2] Shen J F, Bu J J, Ju B, et al. Refining Gaussian Mixture Model Based on Enhanced Manifold Learning. Neurocomputing, 2012, 87: 19-25 [3] Oliveira H, Caeiro J J, Correia P L. Improved Road Crack Detection Based on One-Class Parzen Density Estimation and Entropy Reduction // Proc of the 17thInternational Conference on Image Processing. Hong Kong, China, 2010: 2201-2204 [4] Cyganek B. One-Class Support Vector Ensembles for Image Segmentation and Classification. Journal of Mathematical Imaging and Vision, 2012, 42(2/3): 103-117 [5] Wang C K, Huang I H, Hsu C H. A Novel Approach for Raising the Accuracy of SVDD // Proc of the International Conference on Computing, Measurement, Control and Sensor Network. Taiyuan, China, 2012: 241-244 [6] Sakla W, Chan A, Ji J, et al. An SVDD-Based Algorithm for Target Detection in Hyperspectral Imagery.Geoscience and Remote Sensing Letters, 2011, 8(2): 384-388 [7] Hu Z P, Feng K. An Adaptive One-Class Classification Algorithm Based on Multi-resolution Minimum Spanning Tree Model in High-Dimensional Space. Acta Automatica Sinica, 2012, 38(5): 769-775 (in Chinese) (胡正平,冯 凯.高维空间多分辨率最小生成树模型的自适应一类分类算法.自动化学报, 2012, 38(5): 769-775) [8] Zou H, Hastie T, Tibshirani R. Sparse Principal Component Analysis. Journal of Computational and Graphical Statistics, 2006, 15(2): 265-286 [9] Martinez A M, Kak A C. PCA versus LDA.Trans on Pattern Analysis and Machine Intelligence, 2001, 23(2): 228-233 [10] He X F, Niyogi P. Locality Preserving Projections(LPP)[EB/OL]. [2013-08-30]. http://www.cs.uchicago.edu/files/tr_authentic/TR-2002-09.pdf [11] Yang Y, Nie F P, Xiang S M, et al. Local and Global Regressive Mapping for Manifold Learning with Out-of-Sample Extrapolation // Proc of the 24th American Association for Artificial Intelligence Conference on Artificial Intelligence. Atlanta, USA, 2010: 649-654 [12] Han Y H, Xu Z W, Ma Z G, et al. Image Classification with Manifold Learning for Out-of-Sample Data. Signal Processing, 2013, 93(8): 2169-2177 [13] Bengio Y, Paiement J F, Vincent P, et al. Out-of-Sample Extensions for LLE, ISOMAP, MDS, Eigenmaps and Spectral Clustering[EB/OL]. [2013-08-30]. http://www.iro.umontreal.ca/~lisa/pointeurs/tr1238.pdf [14] Saul L K, Roweis S T. Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds. Journal of Machine Lear-ning Research, 2003, 4: 119-155 [15] Schlkopf B, Smola A, Müller K. Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation, 1998, 10(5): 1299-1319
2015, Vol. 28 
