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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Distance measure is quite important for pattern recognition. Utilizing invariance in image data, tangent distance is very powerful in classifying handwritten digits. For this measure a set of invariant transformations must be known a priori. But in many practical problems, it is very difficult to know these transformations. In this paper, an algorithm is proposed to approximate the invariant tangent distance exclusively from the data. By virtue of ideas arising from manifold learning, the algorithm needs no prior transformations and can be applied to more classification problems. k-nearest neighbor rule based on the new distance are implemented for classification problems. Experimental results on synthetic and real datasets illustrate its validity. In order to achieve good generalization with neural networks overfitting must be controlled. Weight penalty factors are one common method of providing this control. However, using weight penalties creates the additional search problem of finding the optimal penalty factors. MacKay [5] proposed an approximate Bayesian framework for training neural networks, in which penalty factors are treated as hyperparameters and found in an iterative search. However, for classification networks trained with cross-entropy error, this search is slow and unstable, and it is not obvious how to improve it. This paper describes and compares several strategies for controlling this search. Some of these strategies greatly improve the speed and stability of the search. Test runs on a range of tasks are described.