Sparse subspace clustering via group sparse coding

We propose in this paper a novel sparse subspace clustering method that regularizes sparse subspace representation by exploiting the structural sharing between tasks and data points via group sparse coding. We derive simple, provably convergent, and computationally efficient algorithms for solving the proposed group formulations. We demonstrate the advantage of the framework on three challenging benchmark datasets ranging from medical record data to image and text clustering and show that they consistently outperforms rival methods.

Human identification from ECG signals via sparse representation of local segments

This work proposes a novel framework to extract compact and discriminative features from Electrocardiogram (ECG) signals for human identification based on sparse representation of local segments. Specifically, local segments extracted from an ECG signal are projected to a small number of basic elements in a dictionary, which is learned from training data. A final representation is extracted by performing a max pooling procedure over all the sparse coefficient vectors in the ECG signal. Unlike most of existing methods for human identification from ECG signals which require segmentation of individual heartbeats or extraction of fiducial points, the proposed method does not need to segment individual heartbeats or detect any fiducial points. The method achieves an 99.48% accuracy on a 100 subjects dataset constructed from a publicly available database, which demonstrates that both local and global structural information are well captured to characterize the ECG signals.

Learning sparse latent representation and distance metric for image retrieval

The performance of image retrieval depends critically on the semantic representation and the distance function used to estimate the similarity of two images. A good representation should integrate multiple visual and textual (e.g., tag) features and offer a step closer to the true semantics of interest (e.g., concepts). As the distance function operates on the representation, they are interdependent, and thus should be addressed at the same time. We propose a probabilistic solution to learn both the representation from multiple feature types and modalities and the distance metric from data. The learning is regularised so that the learned representation and information-theoretic metric will (i) preserve the regularities of the visual/textual spaces, (ii) enhance structured sparsity, (iii) encourage small intra-concept distances, and (iv) keep inter-concept images separated. We demonstrate the capacity of our method on the NUS-WIDE data. For the well-studied 13 animal subset, our method outperforms state-of-the-art rivals. On the subset of single-concept images, we gain 79:5% improvement over the standard nearest neighbours approach on the MAP score, and 45.7% on the NDCG.

Sparse Representations of Image via Overcomplete Dictionary Learned by Adaptive Non-orthogonal Sparsifying Transform

How to learn an over complete dictionary for sparse representations of image is an important topic in machine learning, sparse coding, blind source separation, etc. The so-called K-singular value decomposition (K-SVD) method [3] is powerful for this purpose, however, it is too time-consuming to apply. Recently, an adaptive orthogonal sparsifying transform (AOST) method has been developed to learn the dictionary that is faster. However, the corresponding coefficient matrix may not be as sparse as that of K-SVD. For solving this problem, in this paper, a non-orthogonal iterative match method is proposed to learn the dictionary. By using the approach of sequentially extracting columns of the stacked image blocks, the non-orthogonal atoms of the dictionary are learned adaptively, and the resultant coefficient matrix is sparser. Experiment results show that the proposed method can yield effective dictionaries and the resulting image representation is sparser than AOST.

Nonnegative Blind Source Separation by Sparse Component Analysis Based on Determinant Measure

The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many real-world signals are sparse, we deal with NBSS by sparse component analysis. First, a determinant-based sparseness measure, named D-measure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into row-to-row optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISM-QP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method.

Blind Spectral Unmixing Based on Sparse Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a widely used method for blind spectral unmixing (SU), which aims at obtaining the endmembers and corresponding fractional abundances, knowing only the collected mixing spectral data. It is noted that the abundance may be sparse (i.e., the endmembers may be with sparse distributions) and sparse NMF tends to lead to a unique result, so it is intuitive and meaningful to constrain NMF with sparseness for solving SU. However, due to the abundance sum-to-one constraint in SU, the traditional sparseness measured by L0/L1-norm is not an effective constraint any more. A novel measure (termed as S-measure) of sparseness using higher order norms of the signal vector is proposed in this paper. It features the physical significance. By using the S-measure constraint (SMC), a gradient-based sparse NMF algorithm (termed as NMF-SMC) is proposed for solving the SU problem, where the learning rate is adaptively selected, and the endmembers and abundances are simultaneously estimated. In the proposed NMF-SMC, there is no pure index assumption and no need to know the exact sparseness degree of the abundance in prior. Yet, it does not require the preprocessing of dimension reduction in which some useful information may be lost. Experiments based on synthetic mixtures and real-world images collected by AVIRIS and HYDICE sensors are performed to evaluate the validity of the proposed method.

Mixing Matrix Estimation From Sparse Mixtures With Unknown Number of Sources

In blind source separation, many methods have been proposed to estimate the mixing matrix by exploiting sparsity. However, they often need to know the source number a priori, which is very inconvenient in practice. In this paper, a new method, namely nonlinear projection and column masking (NPCM), is proposed to estimate the mixing matrix. A major advantage of NPCM is that it does not need any knowledge of the source number. In NPCM, the objective function is based on a nonlinear projection and its maxima just correspond to the columns of the mixing matrix. Thus a column can be estimated first by locating a maximum and then deflated by a masking operation. This procedure is repeated until the evaluation of the objective function decreases to zero dramatically. Thus the mixing matrix and the number of sources are estimated simultaneously. Because the masking procedure may result in some small and useless local maxima, particle swarm optimization (PSO) is introduced to optimize the objective function. Feasibility and efficiency of PSO are also discussed. Comparative experimental results show the efficiency of NPCM, especially in the cases where the number of sources is unknown and the sources are relatively less sparse.

Semi-supervised classification based on subspace sparse representation

Graph plays an important role in graph-based semi-supervised classification. However, due to noisy and redundant features in high-dimensional data, it is not a trivial job to construct a well-structured graph on high-dimensional samples. In this paper, we take advantage of sparse representation in random subspaces for graph construction and propose a method called Semi-Supervised Classification based on Subspace Sparse Representation, SSC-SSR in short. SSC-SSR first generates several random subspaces from the original space and then seeks sparse representation coefficients in these subspaces. Next, it trains semi-supervised linear classifiers on graphs that are constructed by these coefficients. Finally, it combines these classifiers into an ensemble classifier by minimizing a linear regression problem. Unlike traditional graph-based semi-supervised classification methods, the graphs of SSC-SSR are data-driven instead of man-made in advance. Empirical study on face images classification tasks demonstrates that SSC-SSR not only has superior recognition performance with respect to competitive methods, but also has wide ranges of effective input parameters.

Generalised damage identification scheme via sparse representation

Structures inevitably deteriorate during their service lives. Therefore, the methods capable of identifying and assessing various damages in a structure timely and accurately have drawn increasing attention. From a broader perspective, structural damage identification problem can be regarded as a pattern recognition problem by using sparse representation techniques. The unknown signal/feature from a damaged structure can be associated to a known type of signal/feature in a “dictionary”, leading to damage identification. From this new angle, an innovative damage identification scheme has been proposed by the authors. In this paper, two important techniques of this scheme are further discussed, namely the construction of dictionary and the choice of parameters. The numerical simulated soil-pipe system is used for verifying the performance of the proposed method. The results demonstrate that this damage identification scheme will be a promising tool for structural health monitoring.