Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Using Discriminant Eigenfeatures for Image Retrieval
IEEE Transactions on Pattern Analysis and Machine Intelligence
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fractional-Step Dimensionality Reduction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiclass Linear Dimension Reduction by Weighted Pairwise Fisher Criteria
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Online and batch learning of pseudo-metrics
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Face Recognition Using Laplacianfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization
ICML '06 Proceedings of the 23rd international conference on Machine learning
Subclass Discriminant Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Dimensionality Reduction of Multimodal Labeled Data by Local Fisher Discriminant Analysis
The Journal of Machine Learning Research
Information-theoretic metric learning
Proceedings of the 24th international conference on Machine learning
Journal of Cognitive Neuroscience
Bayes Optimality in Linear Discriminant Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Metric embedding for kernel classification rules
Proceedings of the 25th international conference on Machine learning
Principal Component Analysis Based on L1-Norm Maximization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust linear dimensionality reduction
IEEE Transactions on Visualization and Computer Graphics
An introduction to kernel-based learning algorithms
IEEE Transactions on Neural Networks
Maxi-Min discriminant analysis via online learning
Neural Networks
Local discriminative distance metrics ensemble learning
Pattern Recognition
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Classic linear dimensionality reduction (LDR) methods, such as principal component analysis (PCA) and linear discriminant analysis (LDA), are known not to be robust against outliers. Following a systematic analysis of the multi-class LDR problem in a unified framework, we propose a new algorithm, called minimal distance maximization (MDM), to address the non-robustness issue. The principle behind MDM is to maximize the minimal between-class distance in the output space. MDM is formulated as a semi-definite program (SDP), and its dual problem reveals a close connection to ''weighted'' LDR methods. A soft version of MDM, in which LDA is subsumed as a special case, is also developed to deal with overlapping centroids. Finally, we drop the homoscedastic Gaussian assumption made in MDM by extending it in a non-parametric way, along with a gradient-based convex approximation algorithm to significantly reduce the complexity of the original SDP. The effectiveness of our proposed methods are validated on two UCI datasets and two face datasets.