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In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…

Quaternion contains one real part and three imaginary parts, which provided a more expressive hypercomplex space for learning knowledge graph. Existing quaternion embedding models measure the plausibility of a triplet either through…

Word embedding, specially with its recent developments, promises a quantification of the similarity between terms. However, it is not clear to which extent this similarity value can be genuinely meaningful and useful for subsequent tasks.…

Deep metric learning seeks to define an embedding where semantically similar images are embedded to nearby locations, and semantically dissimilar images are embedded to distant locations. Substantial work has focused on loss functions and…

Deep metric learning (DML) is a cornerstone of many computer vision applications. It aims at learning a mapping from the input domain to an embedding space, where semantically similar objects are located nearby and dissimilar objects far…

Approximate computing is a computation domain which can be used to trade time and energy with quality and therefore is useful in embedded systems. Energy is the prime resource in battery-driven embedded systems, like robots. Approximate…

Person re identification is a challenging retrieval task that requires matching a person's acquired image across non overlapping camera views. In this paper we propose an effective approach that incorporates both the fine and coarse pose…

An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…

Node embedding methods find latent lower-dimensional representations which are used as features in machine learning models. In the last few years, these methods have become extremely popular as a replacement for manual feature engineering.…

This paper introduces the induced matching distance, a novel topological metric designed to compare discrete structures represented by a symmetric non-negative function. We apply this notion to analyze agent trajectories over time. We use…

Segregation is a highly nuanced concept that researchers have worked to define and measure over the past several decades. Conventional approaches tend to estimate segregation based on residential patterns in a static manner. In this work,…

Vector similarity measures play a fundamental role in various fields, including machine learning, natural language processing, information retrieval, and data mining. These measures quantify the closeness between two vectors in a…

In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor…

Extracting the relevant information by exploiting the spatial data warehouse becomes increasingly hard. In fact, because of the enormous amount of data stored in the spatial data warehouse, the user, usually, don't know what part of the…

Quantifying the distance between datasets is a fundamental question in mathematics and machine learning. We propose \textit{magnitude distance}, a novel distance metric defined on finite datasets using the notion of the \emph{magnitude} of…

We present a novel approach to geolocalising panoramic images on a 2-D cartographic map based on learning a low dimensional embedded space, which allows a comparison between an image captured at a location and local neighbourhoods of the…

We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or…

For many of the physical phenomena around us, we have developed sophisticated models explaining their behavior. Nevertheless, measuring physical properties from visual observations is challenging due to the high number of causally…

Metric learning has become an attractive field for research on the latest years. Loss functions like contrastive loss, triplet loss or multi-class N-pair loss have made possible generating models capable of tackling complex scenarios with…

Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…