Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consist of an incomplete set of distances and the output is a set of points in Euclidean space realizing those given distances. We survey the theory of Euclidean distance geometry and its most important applications, with special emphasis o...

Human-elephant conflict is a major problem leading to crop damage, human death and injuries caused by elephants, and elephants being killed by humans. In this paper, we propose an automated unsupervised elephant image detection system (EIDS) as a solution to human-elephant conflict in the context of elephant conservation. The elephant's image is captured in the forest border areas and is sent t...

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...

A Discriminative Deep Forest (DisDF) as a metric learning algorithm is proposed in the paper. It is based on the Deep Forest or gcForest proposed by Zhou and Feng and can be viewed as a gcForest modification. The case of the fully supervised learning is studied when the class labels of individual training examples are known. The main idea underlying the algorithm is to assign weights to decisio...

In this paper we introduce three methods for re-scaling data sets aiming at improving the likelihood of clustering validity indexes to return the true number of spherical Gaussian clusters with additional noise features. Our method obtains feature re-scaling factors taking into account the structure of a given data set and the intuitive idea that different features may have different degrees of...

Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.

Most crowd simulations (CS) in architectural spaces are based on rectangular grids with von Neumann or Moore neighborhoods. The distance in the former is defined by the von Neumann metric (vN), and in the latter can be defined by both Manhattan (MM) and Euclidean (ME) metrics. A real space, however, is not limited to right angles. How does the rotation of the grid influence the simulation? Whic...

Content Based Image Retrieval (CBIR) is a process in which for a given query image similar images will be retrieved based on the image content similarity. Image content refers to its visual features, which are mathematical representations of a digital image. The image retrieval task primarily depends on image feature extraction and similarity measurement between the feature vectors. The perform...

Over the past decade, Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics, and especially the problem of wireless sensor network localization, have all become very active areas of res...