Sparse representation-based classification (SRC), proposed by , seeks the sparsest decomposition of a test sample over the dictionary of training samples, with classification to the most-contributing class. Because it assumes test samples can be written as linear combinations of their same-class training samples, the success of SRC depends on the size and representativeness of the training set. Our proposed classification algorithm enlarges the training set by using local principal component analysis to approximate the basis vectors of the tangent hyperplane of the class manifold at each training sample. The dictionary in SRC is replaced by a local dictionary that adapts to the test sample and includes training samples and their corresponding tangent basis vectors. We use a synthetic data set and three face databases to demonstrate that this method can achieve higher classification accuracy than SRC in cases of sparse sampling, nonlinear class manifolds, and stringent dimension reduction.
Additionally, there have been many local modifications to the sparse representation framework with objectives other than classification. For example, 's (RSSL) @cite_20 uses the @math -norm for sparse feature extraction, combining high-level semantics with low-level, locality-preserving features. In the feature selection algorithm (CGSSL) by @cite_3 , features are jointly selected using sparse regularization (via the @math -norm) and a non-negative spectral clustering objective. Not only are the selected features sparse; they also are the most discriminative features in terms of predicting the cluster indicators in both the original space and a lower-dimensional subspace on which the data is assumed to lie.
@cite_3 @cite_20
2084028080 2056935845
Many pattern analysis and data mining problems have witnessed high-dimensional data represented by a large number of features, which are often redundant and noisy. Feature selection is one main technique for dimensionality reduction that involves identifying a subset of the most useful features. In this paper, a novel unsupervised feature selection algorithm, named clustering-guided sparse structural learning (CGSSL), is proposed by integrating cluster analysis and sparse structural analysis into a joint framework and experimentally evaluated. Nonnegative spectral clustering is developed to learn more accurate cluster labels of the input samples, which guide feature selection simultaneously. Meanwhile, the cluster labels are also predicted by exploiting the hidden structure shared by different features, which can uncover feature correlations to make the results more reliable. Row-wise sparse models are leveraged to make the proposed model suitable for feature selection. To optimize the proposed formulation, we propose an efficient iterative algorithm. Finally, extensive experiments are conducted on 12 diverse benchmarks, including face data, handwritten digit data, document data, and biomedical data. The encouraging experimental results in comparison with several representative algorithms and the theoretical analysis demonstrate the efficiency and effectiveness of the proposed algorithm for feature selection. To uncover an appropriate latent subspace for data representation, in this paper we propose a novel Robust Structured Subspace Learning (RSSL) algorithm by integrating image understanding and feature learning into a joint learning framework. The learned subspace is adopted as an intermediate space to reduce the semantic gap between the low-level visual features and the high-level semantics. To guarantee the subspace to be compact and discriminative, the intrinsic geometric structure of data, and the local and global structural consistencies over labels are exploited simultaneously in the proposed algorithm. Besides, we adopt the @math -norm for the formulations of loss function and regularization respectively to make our algorithm robust to the outliers and noise. An efficient algorithm is designed to solve the proposed optimization problem. It is noted that the proposed framework is a general one which can leverage several well-known algorithms as special cases and elucidate their intrinsic relationships. To validate the effectiveness of the proposed method, extensive experiments are conducted on diversity datasets for different image understanding tasks, i.e., image tagging, clustering, and classification, and the more encouraging results are achieved compared with some state-of-the-art approaches.