The celebrated Gini(-Simpson) biodiversity index has found very useful applications in ecology, bio-environmetrics, econometry, psychometry, genetics, and lately in bioinformatics as well. In such applications, mostly, categorical data models, without possibly an ordering of the categories, crop up, which may preempt routine use of conventional measures of quantitative diversity analysis. Furth...

Consider a random vector (X ′, Y )′, where X is d-dimensional and Y is onedimensional. We assume that Y is subject to random right censoring. The aim of this paper is twofold. First we propose a new estimator of the joint distribution of (X ′, Y )′. This estimator overcomes the common curse-of-dimensionality problem, by using a new dimension reduction technique. Second we assume that the relati...

With the development of the web, large numbers of documents are available on the Internet. Digital libraries, news sources and inner data of companies surge more and more. Automatic text categorization becomes more and more important for dealing with massive data. However the major problem of text categorization is the high dimensionality of the feature space. At present there are many methods ...

Many similarity measures for multimedia retrieval, decision support, and data mining are based on underlying vector spaces of high dimensionality. Data-partitioning index methods for such spaces (e.g. grid-les, quad-trees, R-trees, X-trees, etc.) generally work well for low-dimensional spaces, but perform poorly as dimensionality increases|a phenomenon which has become known as thèdimensional c...

In this paper, we will examine the problem of distance function computation and indexing uncertain data in high dimensionality for nearest neighbor and range queries. Because of the inherent noise in uncertain data, traditional distance function measures such as the Lqmetric and their probabilistic variants are not qualitatively effective. This problem is further magnified by the sparsity issue...

This document describes the research I have done since October 1995 for my PhD thesis at the Dept. of Computer Science, University of Sheffield, U.K., which I expect to complete by October/November 1999. My thesis research has involved two generic fields of machine learning: dimensionality reduction and sequential data reconstruction, which I have approached from the common point of view of lat...

ÐSpatial queries in high-dimensional spaces have been studied extensively recently. Among them, nearest-neighbor queries are important in many settings, including spatial databases (Find the k closest cities) and multimedia databases (Find the k most similar images). Previous analyses have concluded that nearest-neighbor search is hopeless in high dimensions due to the notorious acurse of dimen...

In this paper, we will examine the problem of distance function computation and indexing uncertain data in high dimensionality for nearest neighbor and range queries. Because of the inherent noise in uncertain data, traditional distance function measures such as the Lqmetric and their probabilistic variants are not qualitatively effective. This problem is further magnified by the sparsity issue...

let $g=(v,e)$ be a connected simple graph. a labeling $f:v to z_2$ induces two edge labelings $f^+, f^*: e to z_2$ defined by $f^+(xy) = f(x)+f(y)$ and $f^*(xy) = f(x)f(y)$ for each $xy in e$. for $i in z_2$, let $v_f(i) = |f^{-1}(i)|$, $e_{f^+}(i) = |(f^{+})^{-1}(i)|$ and $e_{f^*}(i) = |(f^*)^{-1}(i)|$. a labeling $f$ is called friendly if $|v_f(1)-v_f(0)| le 1$. for a friendly labeling $f$ of...