Collaborative Representation based Classification for Face Recognition

By coding a query sample as a sparse linear combination of all training samples and then classifying it by evaluating which class leads to the minimal coding residual, sparse representation based classification (SRC) leads to interesting results for robust face recognition. It is widely believed that the l1- norm sparsity constraint on coding coefficients plays a key role in the success of SRC, while its use of all training samples to collaboratively represent the query sample is rather ignored. In this paper we discuss how SRC works, and show that the collaborative representation mechanism used in SRC is much more crucial to its success of face classification. The SRC is a special case of collaborative representation based classification (CRC), which has various instantiations by applying different norms to the coding residual and coding coefficient. More specifically, the l1 or l2 norm characterization of coding residual is related to the robustness of CRC to outlier facial pixels, while the l1 or l2 norm characterization of coding coefficient is related to the degree of discrimination of facial features. Extensive experiments were conducted to verify the face recognition accuracy and efficiency of CRC with different instantiations.Comment: It is a substantial revision of a previous conference paper (L. Zhang, M. Yang, et al. "Sparse Representation or Collaborative Representation: Which Helps Face Recognition?" in ICCV 2011

Linear Spatial Pyramid Matching Using Non-convex and non-negative Sparse Coding for Image Classification

Recently sparse coding have been highly successful in image classification mainly due to its capability of incorporating the sparsity of image representation. In this paper, we propose an improved sparse coding model based on linear spatial pyramid matching(SPM) and Scale Invariant Feature Transform (SIFT ) descriptors. The novelty is the simultaneous non-convex and non-negative characters added to the sparse coding model. Our numerical experiments show that the improved approach using non-convex and non-negative sparse coding is superior than the original ScSPM[1] on several typical databases

Supersparse Linear Integer Models for Optimized Medical Scoring Systems

Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer coefficients, and satisfy multiple operational constraints. We present a new method for creating data-driven scoring systems called a Supersparse Linear Integer Model (SLIM). SLIM scoring systems are built by solving an integer program that directly encodes measures of accuracy (the 0-1 loss) and sparsity (the $\ell_0$-seminorm) while restricting coefficients to coprime integers. SLIM can seamlessly incorporate a wide range of operational constraints related to accuracy and sparsity, and can produce highly tailored models without parameter tuning. We provide bounds on the testing and training accuracy of SLIM scoring systems, and present a new data reduction technique that can improve scalability by eliminating a portion of the training data beforehand. Our paper includes results from a collaboration with the Massachusetts General Hospital Sleep Laboratory, where SLIM was used to create a highly tailored scoring system for sleep apnea screeningComment: This version reflects our findings on SLIM as of January 2016 (arXiv:1306.5860 and arXiv:1405.4047 are out-of-date). The final published version of this articled is available at http://www.springerlink.co

Similarity Learning for Provably Accurate Sparse Linear Classification

In recent years, the crucial importance of metrics in machine learning algorithms has led to an increasing interest for optimizing distance and similarity functions. Most of the state of the art focus on learning Mahalanobis distances (requiring to fulfill a constraint of positive semi-definiteness) for use in a local k-NN algorithm. However, no theoretical link is established between the learned metrics and their performance in classification. In this paper, we make use of the formal framework of good similarities introduced by Balcan et al. to design an algorithm for learning a non PSD linear similarity optimized in a nonlinear feature space, which is then used to build a global linear classifier. We show that our approach has uniform stability and derive a generalization bound on the classification error. Experiments performed on various datasets confirm the effectiveness of our approach compared to state-of-the-art methods and provide evidence that (i) it is fast, (ii) robust to overfitting and (iii) produces very sparse classifiers.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

Binary Linear Classification and Feature Selection via Generalized Approximate Message Passing

For the problem of binary linear classification and feature selection, we propose algorithmic approaches to classifier design based on the generalized approximate message passing (GAMP) algorithm, recently proposed in the context of compressive sensing. We are particularly motivated by problems where the number of features greatly exceeds the number of training examples, but where only a few features suffice for accurate classification. We show that sum-product GAMP can be used to (approximately) minimize the classification error rate and max-sum GAMP can be used to minimize a wide variety of regularized loss functions. Furthermore, we describe an expectation-maximization (EM)-based scheme to learn the associated model parameters online, as an alternative to cross-validation, and we show that GAMP's state-evolution framework can be used to accurately predict the misclassification rate. Finally, we present a detailed numerical study to confirm the accuracy, speed, and flexibility afforded by our GAMP-based approaches to binary linear classification and feature selection

Scalable Greedy Algorithms for Transfer Learning

In this paper we consider the binary transfer learning problem, focusing on how to select and combine sources from a large pool to yield a good performance on a target task. Constraining our scenario to real world, we do not assume the direct access to the source data, but rather we employ the source hypotheses trained from them. We propose an efficient algorithm that selects relevant source hypotheses and feature dimensions simultaneously, building on the literature on the best subset selection problem. Our algorithm achieves state-of-the-art results on three computer vision datasets, substantially outperforming both transfer learning and popular feature selection baselines in a small-sample setting. We also present a randomized variant that achieves the same results with the computational cost independent from the number of source hypotheses and feature dimensions. Also, we theoretically prove that, under reasonable assumptions on the source hypotheses, our algorithm can learn effectively from few examples