Fisher's linear discriminant embedded metric learning

In this paper, we propose a novel distance metric learning model, which embeds [email protected]?s linear discriminant into the classical maximum margin criterion. Specifically, given pairs of similar samples and pairs of dissimilar samples, our metric learning model aims to maximize the margin between these two kinds of sample pairs while maintaining a large mean squared distance ratio. In this way, the learned model benefits from exploiting the distributions of sample pairs and thus becomes more reliable and effective. Furthermore, the optimization problem of our model can be solved efficiently by a proposed generic iterative approximate method. The effectiveness of our model is demonstrated on various datasets including a challenging face verification dataset called Labeled Faces in the Wild.

[1]  Cordelia Schmid,et al.  Is that you? Metric learning approaches for face identification , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[2]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[3]  Peng Li,et al.  Similarity Metric Learning for Face Recognition , 2013, 2013 IEEE International Conference on Computer Vision.

[4]  Aleix M. Martínez,et al.  Bayes Optimality in Linear Discriminant Analysis , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Kilian Q. Weinberger,et al.  Distance Metric Learning for Large Margin Nearest Neighbor Classification , 2005, NIPS.

[6]  Jian Sun,et al.  Blessing of Dimensionality: High-Dimensional Feature and Its Efficient Compression for Face Verification , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[7]  Marwan Mattar,et al.  Labeled Faces in the Wild: A Database forStudying Face Recognition in Unconstrained Environments , 2008 .

[8]  Shenghuo Zhu,et al.  Large Scale Strongly Supervised Ensemble Metric Learning, with Applications to Face Verification and Retrieval , 2012, ArXiv.

[9]  Inderjit S. Dhillon,et al.  Information-theoretic metric learning , 2006, ICML '07.

[10]  Geoffrey E. Hinton,et al.  Neighbourhood Components Analysis , 2004, NIPS.

[11]  Peng Li,et al.  Distance Metric Learning with Eigenvalue Optimization , 2012, J. Mach. Learn. Res..

[12]  Li Bai,et al.  Cosine Similarity Metric Learning for Face Verification , 2010, ACCV.

[13]  Yi Liu,et al.  An Efficient Algorithm for Local Distance Metric Learning , 2006, AAAI.

[14]  Jason J. Corso,et al.  Efficient max-margin metric learning , 2012 .

[15]  Dacheng Tao,et al.  Asymptotic Generalization Bound of Fisher’s Linear Discriminant Analysis , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Yoram Singer,et al.  Online and batch learning of pseudo-metrics , 2004, ICML.

[17]  V. Vapnik,et al.  Bounds on Error Expectation for Support Vector Machines , 2000, Neural Computation.

[18]  Thorsten Joachims,et al.  Learning a Distance Metric from Relative Comparisons , 2003, NIPS.

[19]  Matthijs C. Dorst.  Distinctive Image Features from Scale-Invariant Keypoints , 2011 .

[20]  David J. Fleet,et al.  Hamming Distance Metric Learning , 2012, NIPS.

[21]  Wei Liu,et al.  Learning Distance Metrics with Contextual Constraints for Image Retrieval , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[22]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[23]  Michael I. Jordan,et al.  Distance Metric Learning with Application to Clustering with Side-Information , 2002, NIPS.

[24]  Amir Globerson,et al.  Metric Learning by Collapsing Classes , 2005, NIPS.

[25]  Shiguang Shan,et al.  Fusing Robust Face Region Descriptors via Multiple Metric Learning for Face Recognition in the Wild , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.