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

Learning Adaptive Discriminative Correlation Filters via Temporal Consistency Preserving Spatial Feature Selection for Robust Visual Tracking

With efficient appearance learning models, Discriminative Correlation Filter (DCF) has been proven to be very successful in recent video object tracking benchmarks and competitions. However, the existing DCF paradigm suffers from two major issues, i.e., spatial boundary effect and temporal filter degradation. To mitigate these challenges, we propose a new DCF-based tracking method. The key innovations of the proposed method include adaptive spatial feature selection and temporal consistent constraints, with which the new tracker enables joint spatial-temporal filter learning in a lower dimensional discriminative manifold. More specifically, we apply structured spatial sparsity constraints to multi-channel filers. Consequently, the process of learning spatial filters can be approximated by the lasso regularisation. To encourage temporal consistency, the filter model is restricted to lie around its historical value and updated locally to preserve the global structure in the manifold. Last, a unified optimisation framework is proposed to jointly select temporal consistency preserving spatial features and learn discriminative filters with the augmented Lagrangian method. Qualitative and quantitative evaluations have been conducted on a number of well-known benchmarking datasets such as OTB2013, OTB50, OTB100, Temple-Colour, UAV123 and VOT2018. The experimental results demonstrate the superiority of the proposed method over the state-of-the-art approaches

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