Organizing Web search results into a hierarchy of topics and sub-topics facilitates browsing the collection and locating results of interest. In this paper, we propose a new hierarchical monothetic clustering algorithm to build a topic hierarchy for a collection of search results retrieved in response to a query. At every level of the hierarchy, the new algorithm progressively identifies topics in a way that maximizes the coverage while maintaining distinctiveness of the topics. We refer the proposed algorithm to as DisCover. Evaluating the quality of a topic hierarchy is a non-trivial task, the ultimate test being user judgment. We use several objective measures such as coverage and reach time for an empirical comparison of the proposed algorithm with two other monothetic clustering algorithms to demonstrate its superiority. Even though our algorithm is slightly more computationally intensive than one of the algorithms, it generates better hierarchies. Our user studies also show that the proposed algorithm is superior to the other algorithms as a summarizing and browsing tool.

Linear projections for dimensionality reduction, computed using linear discriminant analysis (LDA), are commonly based on optimization of certain separability criteria in the output space. The resulting optimization problem is linear, but these separability criteria are not directly related to the classification accuracy in the output space. Consequently, a trial and error procedure has to be invoked, experimenting with different separability criteria that differ in the weighting function used and selecting the one that performed best on the training set. Often, even the best weighting function among the trial choices results in poor classification of data in the subspace. In this short paper, we introduce the concept of fractional dimensionality and develop an incremental procedure, called the fractional-step LDA (F-LDA) to reduce the dimensionality in fractional steps. The F-LDA algorithm is more robust to the selection of weighting function and for any given weighting function, it finds a subspace in which the classification accuracy is higher than that obtained using LDA.

Dimensionality reduction is the process of mapping high-dimension patterns to a lower dimension subspace. When done prior to classification, estimates obtained in the lower dimension subspace are more reliable. For some classifiers, there is also an improvement in performance due to the removal of the diluting effect of redundant information. A majority of the present approaches to dimensionality reduction are based on scatter matrices or other statistics of the data which do not directly correlate to classification accuracy. The optimality criteria of choice for the purposes of classification is the Bayes error. Usually however, Bayes error is difficult to express analytically. We propose an optimality criteria based on an approximation of the Bayes error and use it to formulate a linear and a nonlinear method of dimensionality reduction. The nonlinear method we propose, relies on using a multilayered perceptron which produces as output the lower dimensional representation. It thus differs from autoassociative like multilayered perceptrons which have been proposed and used for dimensionality reduction. Our results show that the nonlinear method is, as anticipated, superior to the linear method in that it can perform unfolding of a nonlinear manifold. In addition, the nonlinear method we propose provides substantially better lower dimension representation (for classification purposes) than Fisher's linear discriminant (FLD) and two other nonlinear methods of dimensionality reduction that are often used.

Dimensionality reduction is the process of mapping high dimensional patterns to a lower dimensional manifold and is typically used for visualization or as a preprocessing step in classification applications. From a classification viewpoint, the rate of increase of Bayes error serves as an ideal choice to measure the loss of information relevant to classification. Motivated by that, we present a multilayer perceptron which produces as output the lower dimensional representation. The multilayer perceptron is trained so as to minimize the classification error in the subspace. It thus differs from autoassociative like multilayer perceptrons which have been proposed and used for dimensionality reduction. We examine the performance of the proposed method of dimensionality reduction and the effect that varying the parameters have on the algorithm.

In this article we study the effect of dynamically modifying the weight matrix on the performance of a neural associative memory. The dynamic modification is implemented by adding, at each step, the outer product of the current state, scaled by a suitable constant eta, to the correlation weight matrix. For single-shot synchronous dynamics, we analytically obtain the optimal value of eta. Although knowledge of the noise percentage is required for calculating the optimal value of eta, a fairly good choice of eta can be made even when the amount of noise is not known. Experimental results are provided in support of the analysis. The efficacy of the proposed modification is also experimentally verified for the case of asynchronous updating with transient length > 1.