Semi-Supervised Sparse Coding

Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the manifold structure spanned by the data set of both labeled and unlabeled samples and the constraints provided by the labels of the labeled samples, we learn the variable class labels for all the samples. Furthermore, to improve the discriminative ability of the learned sparse codes, we assume that the class labels could be predicted from the sparse codes directly using a linear classifier. By solving the codebook, sparse codes, class labels and classifier parameters simultaneously in a unified objective function, we develop a semi-supervised sparse coding algorithm. Experiments on two real-world pattern recognition problems demonstrate the advantage of the proposed methods over supervised sparse coding methods on partially labeled data sets

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

Sparse Coding on Stereo Video for Object Detection

Deep Convolutional Neural Networks (DCNN) require millions of labeled training examples for image classification and object detection tasks, which restrict these models to domains where such datasets are available. In this paper, we explore the use of unsupervised sparse coding applied to stereo-video data to help alleviate the need for large amounts of labeled data. We show that replacing a typical supervised convolutional layer with an unsupervised sparse-coding layer within a DCNN allows for better performance on a car detection task when only a limited number of labeled training examples is available. Furthermore, the network that incorporates sparse coding allows for more consistent performance over varying initializations and ordering of training examples when compared to a fully supervised DCNN. Finally, we compare activations between the unsupervised sparse-coding layer and the supervised convolutional layer, and show that the sparse representation exhibits an encoding that is depth selective, whereas encodings from the convolutional layer do not exhibit such selectivity. These result indicates promise for using unsupervised sparse-coding approaches in real-world computer vision tasks in domains with limited labeled training data

On the Sample Complexity of Predictive Sparse Coding

The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task. Predictive sparse coding algorithms recently have demonstrated impressive performance on a variety of supervised tasks, but their generalization properties have not been studied. We establish the first generalization error bounds for predictive sparse coding, covering two settings: 1) the overcomplete setting, where the number of features k exceeds the original dimensionality d; and 2) the high or infinite-dimensional setting, where only dimension-free bounds are useful. Both learning bounds intimately depend on stability properties of the learned sparse encoder, as measured on the training sample. Consequently, we first present a fundamental stability result for the LASSO, a result characterizing the stability of the sparse codes with respect to perturbations to the dictionary. In the overcomplete setting, we present an estimation error bound that decays as \tilde{O}(sqrt(d k/m)) with respect to d and k. In the high or infinite-dimensional setting, we show a dimension-free bound that is \tilde{O}(sqrt(k^2 s / m)) with respect to k and s, where s is an upper bound on the number of non-zeros in the sparse code for any training data point.Comment: Sparse Coding Stability Theorem from version 1 has been relaxed considerably using a new notion of coding margin. Old Sparse Coding Stability Theorem still in new version, now as Theorem 2. Presentation of all proofs simplified/improved considerably. Paper reorganized. Empirical analysis showing new coding margin is non-trivial on real dataset