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.
The approach of using tangent hyperplanes for pattern recognition is not new. When the data is assumed to lie on a low-dimensional manifold, local tangent hyperplanes are a simple and intuitive approach to enhancing the data set and gaining insight into the manifold structure. Our proposed method is very much related to (TDC) @cite_16 @cite_12 @cite_24 , which constructs local tangent hyperplanes of the class manifolds, computes the distances between these hyperplanes and the given test sample, and then classifies the test sample to the class with the closest hyperplane. We show in Section that our proposed method's integration of tangent hyperplane basis vectors into the sparse representation framework generally outperforms TDC.
@cite_24 @cite_16 @cite_12
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Motivated by image perturbation and the geometry of manifolds, we present a novel method combining these two elements. First, we form a tangent space from a set of perturbed images and observe that the tangent space admits a vector space structure. Second, we embed the approximated tangent spaces on a Grassmann manifold and employ a chordal distance as the means for comparing subspaces. The matching process is accelerated using a coarse to fine strategy. Experiments on the FERET database suggest that the proposed method yields excellent results using both holistic and local features. Specifically, on the FERET Dup2 data set, our proposed method achieves 83.8 rank 1 recognition: to our knowledge the currently the best result among all non-trained methods. Evidence is also presented that peak recognition performance is achieved using roughly 100 distinct perturbed images. This brief paper presents a novel method for low-resolution face recognition. We introduce a generalized bipartite graph to discretely approximate the underlying manifold structure of face sets with different resolutions. Unlike traditional graph-based methods that only construct the graph based on one sample set, the proposed method constructs the generalized bipartite graph on two heterogeneous sample sets and contains more completed information. Our method learns a couple of mappings that project the face sets with different dimensions into a unified feature space which favors the task of classification. Specifically, in this unified space, our method preserves within-class local geometrical structure according to the network topology of the generalized bipartite graph and maximizes between-class separability at the same time. Experimental results on two benchmark face databases demonstrate the effectiveness of our proposed algorithm. HighlightsWe propose a novel method for low-resolution face recognition.We introduce the generalized bipartite graph to approximate the manifold structure.Our method preserves within-class local geometrical structure.Our method maximizes between-class separability.Low and high resolution faces are projected to a unified discriminative subspace. We consider the problem of retrieving the database points nearest to a given hyperplane query without exhaustively scanning the entire database. For this problem, we propose two hashing-based solutions. Our first approach maps the data to 2-bit binary keys that are locality sensitive for the angle between the hyperplane normal and a database point. Our second approach embeds the data into a vector space where the euclidean norm reflects the desired distance between the original points and hyperplane query. Both use hashing to retrieve near points in sublinear time. Our first method's preprocessing stage is more efficient, while the second has stronger accuracy guarantees. We apply both to pool-based active learning: Taking the current hyperplane classifier as a query, our algorithm identifies those points (approximately) satisfying the well-known minimal distance-to-hyperplane selection criterion. We empirically demonstrate our methods' tradeoffs and show that they make it practical to perform active selection with millions of unlabeled points. Local learning of sparse image models has proved to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean distance as a dissimilarity metric. However, the Euclidean distance may not always be a good dissimilarity measure for comparing data samples lying on a manifold. In this paper, we propose two algorithms for determining a local subset of training samples from which a good local model can be computed for reconstructing a given input test sample, where we consider the underlying geometry of the data. The first algorithm, called adaptive geometry-driven nearest neighbor search (AGNN), is an adaptive scheme, which can be seen as an out-of-sample extension of the replicator graph clustering method for local model learning. The second method, called geometry-driven overlapping clusters (GOCs), is a less complex nonadaptive alternative for training subset selection. The proposed AGNN and GOC methods are evaluated in image superresolution and shown to outperform spectral clustering, soft clustering, and geodesic distance-based subset selection in most settings.