If A is a real symmetric matrix and P is an orthogonal projection onto a hyperplane, then we derive a formula for the Moore-Penrose inverse of PAP . As an application, we obtain a formula for the MoorePenrose inverse of a Euclidean distance matrix (EDM) which generalizes formulae for the inverse of a EDM in the literature. To an invertible spherical EDM, we associate a Laplacian matrix (which w...

We consider distance-based similarity measures for real-valued vectors of interest in kernel-based machine learning algorithms. In particular, a truncated Euclidean similarity measure and a self-normalized similarity measure related to the Canberra distance. It is proved that they are positive semi-definite (p.s.d.), thus facilitating their use in kernel-based methods, like the Support Vector M...

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if the original manifold is not Euclidean. In this paper, we propose to learn the...

We suggest the use of alternative distance measures for similarity based classification in Learning Vector Quantization. Divergences can be employed whenever the data consists of non-negative normalized features, which is the case for, e.g., spectral data or histograms. As examples, we derive gradient based training algorithms in the framework of Generalized Learning Vector Quantization based o...

This paper presents a novel and robust algorithm that retrieves the rotation angle between two different patterns, together with their similarity degree. The result is optimal in the sense that it minimizes the euclidean distance between the two images. This approach is based on Zernike moments and constitutes a new way to compare two Zernike descriptors that improves standard Euclidean approac...

基金项目:本项目得到国家自然科学基金项目(81170118、61003193)、湖南省科技计划资助项目(2010GK3064)、国家“八六三”高技术 研究发展计划(2012AA120903)、浙江省科技厅公益项目(No.2011C21058)的资助。 作者简介:解聪(1989—),男,硕士研究生,主要研究方向为医学影像可视化;雷辉(1977-),女,讲师,硕士,主要研究方向:图像 处理,小波分析;徐星(1987—),男,硕士研究生,主要研究方向为医学影像可视化;陈伟锋(1983—),男,博士,主要研究方向为科 学计算可视化;陈海东(1987—),男,博士,主要研究方向为科学计算可视化;杨劲松(1974—),男,博士,主要研究方向为放射学及 放射肿瘤学的基础临床研究;严丹方(1984—),女,硕士研究生,主要研究方向为放射学及放射肿瘤学的基础临床研究;陈为(1976—), 男,博士,教...

We study different types of aggregation operators such as the ordered weighted averaging (OWA) operator and the generalized OWA (GOWA) operator. We analyze the use of OWA operators in the Minkowski distance. We will call these new distance aggregation operator the Minkowski ordered weighted averaging distance (MOWAD) operator. We give a general overview of this type of generalization and study ...

An n-point metric space (X,D) can be represented by an n × n table specifying the distances. Such tables arise in many diverse areas. For example, consider the following scenario in microbiology: X is a collection of bacterial strains, and for every two strains, one is given their dissimilarity (computed, say, by comparing their DNA). It is difficult to see any structure in a large table of num...