Browsing by Author "Ye, Jieping"
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Item A new optimization criterion for generalized discriminant analysis on undersampled problems(2003-06-10) Ye, Jieping; Janardan, Ravi; Park, Cheonghee; Park, HaesunWe present a new optimization criterion for discriminant analysis. The new criterion extends the optimization criteria of the classical linear discriminant analysis (LDA) by introducing the pseudo-inverse when the scatter matrices are singular. It is applicable regardless of the relative sizes of the data dimension and sample size,overcoming a limitation of the classical LDA. Recently, a new algorithm called LDA/GSVD for structure-preserving dimension reduction has been introduced, which extends the classical LDA to very high-dimensional undersampled problems by using the generalized singular value decomposition (GSVD). The solution from the LDA/GSVD algorithm is a special case of the solution for our generalized criterion in this paper, which is also based on GSVD. We also present an approximate solution for our GSVD-based solution, which reduces computational complexity by finding sub-clusters of each cluster, and using their centroids to capture the structure of each cluster. This reduced problem yields much smaller matrices of which the GSVD can be applied efficiently. Experiments on text data, with up to 7000 dimensions, show that the approximation algorithm produces results that are close to those produced by the exact algorithm.Item Approximate Multiple Protein Structure Alignment Using the Sum-of-Pairs Distance(2003-03-31) Ye, Jieping; Janardan, RaviAn algorithm is presented to compute a multiple structure alignment for a set of proteins and to generate a consensus (pseudo) protein for the set. The algorithm is a heuristic in that it computes an approximation to the optimal multiple structure alignment that minimizes the sum of thepairwise distances between the protein structures. The algorithm chooses an input protein as the initial consensus and computes a correspondence between the protein structures (which are represented as sets of unitvectors) using an approach analogous to the center-star method for multiple sequence alignment. From this correspondence, a set of rotation matrices (optimal for the given correspondence) is derived to align the structures and derive the new consensus. The process is iterated until the sum of pairwise distances converges. The computation of the optimal rotations is itself an iterative process that both makes use of the current consensus and generates simultaneously a new one. This approach is based on an interesting result that allows the sum of all pairwisedistances to be represented compactly as distances to the consensus. Experimental results on several protein families are presented, showing that the algorithm converges quite rapidly.Item Pairwise Protein Structure Alignment Based on an Orientation-Independent Representation of the Backbone Geometry(2003-01-14) Ye, Jieping; Janardan, Ravi; Liu, SongtaoDetermining structural similarities between proteins is animportant problem since it can help identify functional and evolutionary relationships. In this paper, an algorithm is proposed to align two protein structures. Given the protein backbones, the algorithm finds a rigid motion of one backbone onto the other such that large substructures are matched. The algorithm uses a representation of the backbone that is independent of their relative orientations in space and applies dynamic programming to this representation to compute an initial alignment, which is then refined iteratively. Experiments indicate that the algorithm is competitive with two well-known algorithms, namely DALI [12] and LOCK [19].