Browsing by Author "Rosen, J. Ben"

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    Dimension Reduction Based on Centroids and Least Squares for Efficient Processing of Text Data
    (2001-02-08) Jeon, Moongu; Park, Haesun; Rosen, J. Ben
    Dimension reduction in today's vector space based information retrieval system is essential for improving computational efficiency in handling massive data. In our previous work we proposed a mathematical framework for lower dimensional representations of text data in vector space based information retrieval, and a couple of dimension reduction methods using minimization and matrix rank reduction formula. One of our proposed methods is CentroidQR method which utilizes orthogonal transformation on centroids, and the test results showed that its classification results were exactly the same as those of classification with full dimension when a certain classification algorithm is applied. In this paper we discuss in detail the CentroidQR method, and prove mathematically its classification properties with two different similarity measures of L2 and cosine.
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    Exponential Modeling with Unknown Model Order Using Structured Nonlinear Total Least Norm
    (2000-04-07) Zhang, Lei; Park, Haesun; Rosen, J. Ben
    A method based on Structured Nonlinear Total Least Norm is presented for estimating the parameters of exponentially damped sinusoidal signals in noise when the model order is unknown. It is compared to two other existing methods to show its robustness in recovering correct values of parameters when the model order is unknown, in spite of some large errors in measured data.
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    Low Rank Approximation of a Hankel Matrix by Structured Total Least Norm
    (1997) Park, Haesun; Zhang, Lei; Rosen, J. Ben
    The structure preserving rank reduction problem arises in many important applications. The singular value decomposition (SVD), while giving the best low rank approximation to a given matrix, may not be appropriate for these applications since it does not preserve the given structure. We present a new method for structure preserving low rank approximation of a matri.x, which is based on Structured Total Least Norm (STLN). The STLN is an efficient method for obtaining an approximate solution to the overdetermined linear system AX ~ B preserving the given linear structure in .4. or (A I BJ, where errors can occur in both the right hand side matrix B and the matrix A. The approximate solution can be obtained to minimize the error in the Lp norm, where p = l, 2, or oo. An algorithm is described for Hankel structure preserving low rank approximation using STLN with Lp norm. Computational results are presented, which compare performances of the STLN based method for L1 and L2 norms and other existing methods for reduced rank approximation for Hankel matrices.
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    Lower Dimensional Representation of Text Data in Vector Space Based Information Retrieval
    (2000-12-06) Park, Haesun; Jeon, Moongu; Rosen, J. Ben
    Dimension reduction in today's vector space based information retrieval system is essen-tial for improving computational efficiency in handling massive data.In this paper, we propose a mathematical framework for lower dimensional representa-tion of text data in vector space based in-formation retrieval using minimization and matrix rank reduction formula. We illustrate how the commonly used Latent Semantic Indexing based on Singular Value Decom-position (LSI/SVD) can be derived as a method for dimension reduction from our mathematical framework. Then we propose a new approach which is more efficient and effective than LSI/SVD when we have a pri-ori information on the cluster structure of the data. Several advantages of the new meth-ods are discussed over the LSI/SVD in terms of computational efficiency and data representation in the reduced dimensional space.Experimental results are presented to illus-trate the effectiveness of our approach in certain classification problem in reduced di-mensional space. These results were com-puted using an information retrieval test sys-tem we are now developing. The results in-dicate that for a successful lower dimen-sional representation of data, it is important to incorporate a priori knowledge on data in dimension reduction.