Related papers: Spatial Metric Space for Pattern Recognition Probl…

We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…

Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…

This paper is about similarity between objects that can be represented as points in metric measure spaces. A metric measure space is a metric space that is also equipped with a measure. For example, a network with distances between its…

Spatial association and heterogeneity are two critical areas in the research about spatial analysis, geography, statistics and so on. Though large amounts of outstanding methods has been proposed and studied, there are few of them tend to…

In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…

Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two…

We propose a novel deep metric learning method. Differently from many works on this area, we defined a novel latent space obtained through an autoencoder. The new space, namely S-space, is divided into different regions that describe the…

We study the metric structure of walks on graphs, understood as Lipschitz sequences. To this end, a weighted metric is introduced to handle sequences, enabling the definition of distances between walks based on stepwise vertex distances and…

This article presents a new distance for measuring shape dissimilarity between objects. Recent publications introduced the use of eigenvalues of the Laplace operator as compact shape descriptors. Here, we revisit the eigenvalues to define a…

Being a pair of dual concepts, the normalized distance and similarity measures are very important tools for decision-making and pattern recognition under intuitionistic fuzzy sets framework. To be more effective for decision-making and…

The Gromov-Hausdorff distance measures the similarity between two metric spaces by isometrically embedding them into an ambient metric space. We introduce an analogue of this distance for metric spaces endowed with directed structures. The…

Studies on various facets of pattern classification is often imperative while working with multi-dimensional samples pertaining to diverse application scenarios. In this notion, weighted dimension-based distance measure has been one of the…

Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…

Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…

Successive divisions of compact metric spaces appear in many different areas of mathematics such as the construction of self-similar sets, Markov partitions associated with hyperbolic dynamical systems, dyadic cubes associated with a…

A labeled metric space is intuitively speaking a metric space together with a special set of points to be understood as the geometric boundary of the space. We study basic properties of a recently introduced labeled Gromov-Hausdorff…

Inverse Distance Weighted models (IDW) have been widely used for predicting and modeling multidimensional space in multimodal industrial processes. However, the more complex the structure of multidimensional space, the lower the performance…

Classical metric spaces often fail to model data-intensive systems where repetition and frequency of values are meaningful. In applications such as transactional databases, sensor logs, and record linkage, conventional distance measures…

In many computer vision tasks, for example saliency prediction or semantic segmentation, the desired output is a foreground map that predicts pixels where some criteria is satisfied. Despite the inherently spatial nature of this task…

Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the…