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The success of linear discriminant analysis (LDA) is due in part to the simplicity of its formulation, which reduces to a simultaneous diagonalization of two symmetric matrices A and B. However, a fundamental drawback of this approach is that it cannot be efficiently applied wherever the matrix A is singular or when some of the smallest variances in A are due to noise. In this paper, we present a factorization of A-1B and a correlation-based criterion that can be readily employed to solve these problems. We provide detailed derivations for the linear and nonlinear classification problems. The usefulness of the proposed approach is demonstrated thoroughly using a large variety of databases. [ABSTRACT FROM AUTHOR]

Background: Microarray-based tumor classification is characterized by a very large number of features (genes) and small number of samples. In such cases, statistical techniques cannot determine which genes are correlated to each tumor type. A popular solution is the use of a subset of prespecified genes. However, molecular variations are generally correlated to a large number of genes. A gene that is not correlated to some disease may, by combination with other genes, express itself. Results: In this paper, we propose a new classiification strategy that can reduce the effect of overfitting without the need to pre-select a small subset of genes. Our solution works by taking advantage of the information embedded in the testing samples. We note that a well-defined classification algorithm works best when the data is properly labeled. Hence, our classification algorithm will discriminate all samples best when the testing sample is assumed to belong to the correct class. We compare our solution with several well-known alternatives for tumor classification on a variety of publicly available data-sets. Our approach consistently leads to better classification results. Conclusion: Studies indicate that thousands of samples may be required to extract useful statistical information from microarray data. Herein, it is shown that this problem can be circumvented by using the information embedded in the testing samples. [ABSTRACT FROM AUTHOR]

Despite the existence of obstacles in many database applications, traditional spatial query processing assumes that points in space are directly reachable and utilizes the Euclidean distance metric. In this paper, we study spatial queries in the presence of obstacles, where the obstructed distance between two points is defined as the length of the shortest path that connects them without crossing any obstacles. We propose efficient algorithms for the most important query types, namely, range search, nearest neighbours, e ‐distance joins, closest pairs and distance semi‐joins, assuming that both data objects and obstacles are indexed by R‐trees. The effectiveness of the proposed solutions is verified through extensive experiments. [ABSTRACT FROM AUTHOR]