Related papers: Complex-valued embeddings of generic proximity dat…

Metric data structures (distance oracles, distance labeling schemes, routing schemes) and low-distortion embeddings provide a powerful algorithmic methodology, which has been successfully applied for approximation algorithms \cite{llr},…

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.…

Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…

Deep metric learning aims to learn an embedding function, modeled as deep neural network. This embedding function usually puts semantically similar images close while dissimilar images far from each other in the learned embedding space.…

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…

Information theoretic quantities play an important role in various settings in machine learning, including causality testing, structure inference in graphical models, time-series problems, feature selection as well as in providing privacy…

The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…

Neural Networks and related Deep Learning methods are currently at the leading edge of technologies used for classifying objects. However, they generally demand large amounts of time and data for model training; and their learned models can…

The crucial importance of metrics in machine learning algorithms has led to an increasing interest in optimizing distance and similarity functions, an area of research known as metric learning. When data consist of feature vectors, a large…

Many data representations are vectors of continuous values. In particular, deep learning embeddings are data-driven representations, typically either unconstrained in Euclidean space, or constrained to a hypersphere. These may also be…

Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…

Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…

Representation learning for graphs enables the application of standard machine learning algorithms and data analysis tools to graph data. Replacing discrete unordered objects such as graph nodes by real-valued vectors is at the heart of…

The goal of metric learning is to learn a function that maps samples to a lower-dimensional space where similar samples lie closer than dissimilar ones. Particularly, deep metric learning utilizes neural networks to learn such a mapping.…

Embedders play a central role in machine learning, projecting any object into numerical representations that can, in turn, be leveraged to perform various downstream tasks. The evaluation of embedding models typically depends on…

Data clustering, the task of grouping observations according to their similarity, is a key component of unsupervised learning -- with real world applications in diverse fields such as biology, medicine, and social science. Often in these…

This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…

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.…

The classification of big data usually requires a mapping onto new data clusters which can then be processed by machine learning algorithms by means of more efficient and feasible linear separators. Recently, Lloyd et al. have advanced the…

Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…