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

Masking Strategies for Image Manifolds

We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of compressive sensing through emerging imaging sensor platforms for which the power expense grows with the number of pixels acquired. Our goal is for the manifold learned from masked images to resemble its full image counterpart as closely as possible. More precisely, we show that one can indeed accurately learn an image manifold without having to consider a large majority of the image pixels. In doing so, we consider two masking methods that preserve the local and global geometric structure of the manifold, respectively. In each case, the process of finding the optimal masking pattern can be cast as a binary integer program, which is computationally expensive but can be approximated by a fast greedy algorithm. Numerical experiments show that the relevant manifold structure is preserved through the data-dependent masking process, even for modest mask sizes

High Dimensional Data Set Analysis Using a Large-Scale Manifold Learning Approach

Because of technological advances, a trend occurs for data sets increasing in size and dimensionality. Processing these large scale data sets is challenging for conventional computers due to computational limitations. A framework for nonlinear dimensionality reduction on large databases is presented that alleviates the issue of large data sets through sampling, graph construction, manifold learning, and embedding. Neighborhood selection is a key step in this framework and a potential area of improvement. The standard approach to neighborhood selection is setting a fixed neighborhood. This could be a fixed number of neighbors or a fixed neighborhood size. Each of these has its limitations due to variations in data density. A novel adaptive neighbor-selection algorithm is presented to enhance performance by incorporating sparse ℓ 1-norm based optimization. These enhancements are applied to the graph construction and embedding modules of the original framework. As validation of the proposed ℓ1-based enhancement, experiments are conducted on these modules using publicly available benchmark data sets. The two approaches are then applied to a large scale magnetic resonance imaging (MRI) data set for brain tumor progression prediction. Results showed that the proposed approach outperformed linear methods and other traditional manifold learning algorithms

Unsupervised spectral sub-feature learning for hyperspectral image classification

Spectral pixel classification is one of the principal techniques used in hyperspectral image (HSI) analysis. In this article, we propose an unsupervised feature learning method for classification of hyperspectral images. The proposed method learns a dictionary of sub-feature basis representations from the spectral domain, which allows effective use of the correlated spectral data. The learned dictionary is then used in encoding convolutional samples from the hyperspectral input pixels to an expanded but sparse feature space. Expanded hyperspectral feature representations enable linear separation between object classes present in an image. To evaluate the proposed method, we performed experiments on several commonly used HSI data sets acquired at different locations and by different sensors. Our experimental results show that the proposed method outperforms other pixel-wise classification methods that make use of unsupervised feature extraction approaches. Additionally, even though our approach does not use any prior knowledge, or labelled training data to learn features, it yields either advantageous, or comparable, results in terms of classification accuracy with respect to recent semi-supervised methods

Sparse Transfer Learning for Interactive Video Search Reranking

Visual reranking is effective to improve the performance of the text-based video search. However, existing reranking algorithms can only achieve limited improvement because of the well-known semantic gap between low level visual features and high level semantic concepts. In this paper, we adopt interactive video search reranking to bridge the semantic gap by introducing user's labeling effort. We propose a novel dimension reduction tool, termed sparse transfer learning (STL), to effectively and efficiently encode user's labeling information. STL is particularly designed for interactive video search reranking. Technically, it a) considers the pair-wise discriminative information to maximally separate labeled query relevant samples from labeled query irrelevant ones, b) achieves a sparse representation for the subspace to encodes user's intention by applying the elastic net penalty, and c) propagates user's labeling information from labeled samples to unlabeled samples by using the data distribution knowledge. We conducted extensive experiments on the TRECVID 2005, 2006 and 2007 benchmark datasets and compared STL with popular dimension reduction algorithms. We report superior performance by using the proposed STL based interactive video search reranking.Comment: 17 page