Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.Comment: 33 pages, 12 figure

Joint learning and dictionary construction for pattern recognition

We propose a joint representation and classification framework that achieves the dual goal of finding the most discriminative sparse overcomplete encoding and optimal classifier parameters. Formulating an optimization problem that combines the objective function of the classification with the representation error of both labeled and unlabeled data, constrained by sparsity, we propose an algorithm that alternates between solving for subsets of parameters, whilst preserving the sparsity. The method is then evaluated over two important classification problems in computer vision: object categorization of natural images using the Caltech 101 database and face recognition using the Extended Yale B face database. The results show that the proposed method is competitive against other recently proposed sparse overcomplete counterparts and considerably outperforms many recently proposed face recognition techniques when the number training samples is small.<br /

Discriminative Recurrent Sparse Auto-Encoders

We present the discriminative recurrent sparse auto-encoder model, comprising a recurrent encoder of rectified linear units, unrolled for a fixed number of iterations, and connected to two linear decoders that reconstruct the input and predict its supervised classification. Training via backpropagation-through-time initially minimizes an unsupervised sparse reconstruction error; the loss function is then augmented with a discriminative term on the supervised classification. The depth implicit in the temporally-unrolled form allows the system to exhibit all the power of deep networks, while substantially reducing the number of trainable parameters. From an initially unstructured network the hidden units differentiate into categorical-units, each of which represents an input prototype with a well-defined class; and part-units representing deformations of these prototypes. The learned organization of the recurrent encoder is hierarchical: part-units are driven directly by the input, whereas the activity of categorical-units builds up over time through interactions with the part-units. Even using a small number of hidden units per layer, discriminative recurrent sparse auto-encoders achieve excellent performance on MNIST.Comment: Added clarifications suggested by reviewers. 15 pages, 10 figure

Optimal Clustering Framework for Hyperspectral Band Selection

Band selection, by choosing a set of representative bands in hyperspectral image (HSI), is an effective method to reduce the redundant information without compromising the original contents. Recently, various unsupervised band selection methods have been proposed, but most of them are based on approximation algorithms which can only obtain suboptimal solutions toward a specific objective function. This paper focuses on clustering-based band selection, and proposes a new framework to solve the above dilemma, claiming the following contributions: 1) An optimal clustering framework (OCF), which can obtain the optimal clustering result for a particular form of objective function under a reasonable constraint. 2) A rank on clusters strategy (RCS), which provides an effective criterion to select bands on existing clustering structure. 3) An automatic method to determine the number of the required bands, which can better evaluate the distinctive information produced by certain number of bands. In experiments, the proposed algorithm is compared to some state-of-the-art competitors. According to the experimental results, the proposed algorithm is robust and significantly outperform the other methods on various data sets

Generative-Discriminative Low Rank Decomposition for Medical Imaging Applications

In this thesis, we propose a method that can be used to extract biomarkers from medical images toward early diagnosis of abnormalities. Surge of demand for biomarkers and availability of medical images in the recent years call for accurate, repeatable, and interpretable approaches for extracting meaningful imaging features. However, extracting such information from medical images is a challenging task because the number of pixels (voxels) in a typical image is in order of millions while even a large sample-size in medical image dataset does not usually exceed a few hundred. Nevertheless, depending on the nature of an abnormality, only a parsimonious subset of voxels is typically relevant to the disease; therefore various notions of sparsity are exploited in this thesis to improve the generalization performance of the prediction task. We propose a novel discriminative dimensionality reduction method that yields good classification performance on various datasets without compromising the clinical interpretability of the results. This is achieved by combining the modelling strength of generative learning framework and the classification performance of discriminative learning paradigm. Clinical interpretability can be viewed as an additional measure of evaluation and is also helpful in designing methods that account for the clinical prior such as association of certain areas in a brain to a particular cognitive task or connectivity of some brain regions via neural fibres. We formulate our method as a large-scale optimization problem to solve a constrained matrix factorization. Finding an optimal solution of the large-scale matrix factorization renders off-the-shelf solver computationally prohibitive; therefore, we designed an efficient algorithm based on the proximal method to address the computational bottle-neck of the optimization problem. Our formulation is readily extended for different scenarios such as cases where a large cohort of subjects has uncertain or no class labels (semi-supervised learning) or a case where each subject has a battery of imaging channels (multi-channel), \etc. We show that by using various notions of sparsity as feasible sets of the optimization problem, we can encode different forms of prior knowledge ranging from brain parcellation to brain connectivity

State-of-the-art and gaps for deep learning on limited training data in remote sensing

Deep learning usually requires big data, with respect to both volume and variety. However, most remote sensing applications only have limited training data, of which a small subset is labeled. Herein, we review three state-of-the-art approaches in deep learning to combat this challenge. The first topic is transfer learning, in which some aspects of one domain, e.g., features, are transferred to another domain. The next is unsupervised learning, e.g., autoencoders, which operate on unlabeled data. The last is generative adversarial networks, which can generate realistic looking data that can fool the likes of both a deep learning network and human. The aim of this article is to raise awareness of this dilemma, to direct the reader to existing work and to highlight current gaps that need solving.Comment: arXiv admin note: text overlap with arXiv:1709.0030

Pruning Convolutional Neural Networks with Self-Supervision

Convolutional neural networks trained without supervision come close to matching performance with supervised pre-training, but sometimes at the cost of an even higher number of parameters. Extracting subnetworks from these large unsupervised convnets with preserved performance is of particular interest to make them less computationally intensive. Typical pruning methods operate during training on a task while trying to maintain the performance of the pruned network on the same task. However, in self-supervised feature learning, the training objective is agnostic on the representation transferability to downstream tasks. Thus, preserving performance for this objective does not ensure that the pruned subnetwork remains effective for solving downstream tasks. In this work, we investigate the use of standard pruning methods, developed primarily for supervised learning, for networks trained without labels (i.e. on self-supervised tasks). We show that pruned masks obtained with or without labels reach comparable performance when re-trained on labels, suggesting that pruning operates similarly for self-supervised and supervised learning. Interestingly, we also find that pruning preserves the transfer performance of self-supervised subnetwork representations