Related papers: A new class of metrics for learning on real-valued…

Deep semi-supervised learning has been widely implemented in the real-world due to the rapid development of deep learning. Recently, attention has shifted to the approaches such as Mean-Teacher to penalize the inconsistency between two…

A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new ``normalized information distance'', based on the noncomputable notion of…

Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability,…

In Ordinal Classification tasks, items have to be assigned to classes that have a relative ordering, such as positive, neutral, negative in sentiment analysis. Remarkably, the most popular evaluation metrics for ordinal classification tasks…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

For the first time, we introduce "Scaling invariable Benford distance" and "Benford cyclic graph", which can be used to analyze any data set. Using the quantity and the graph, we analyze some date sets with common distributions, such as…

We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…

To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…

Despite successful use in a wide variety of disciplines for data analysis and prediction, machine learning (ML) methods suffer from a lack of understanding of the reliability of predictions due to the lack of transparency and black-box…

Machine Learning has attracted considerable attention throughout the past decade due to its potential to solve far-reaching tasks, such as image classification, object recognition, anomaly detection, and data forecasting. A standard…

Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…

The purpose of this paper is to study more general real-valued functions of two variables than just metrics on a set X. We concentrate mainly on the classes of distances and almost distances. We also introduce the notion of a bridge on the…

Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…

Dempster-Shafer theory is widely applied in uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. A distance between two basic probability assignments(BPAs) presents a measure of performance…

Mukherjee (Pattern Recognition Letters, vol. 32, pp. 824-831, 2011) recently introduced a class of distance functions called weighted t-cost distances that generalize m-neighbor, octagonal, and t-cost distances. He proved that weighted…

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.…

Clustering of motion trajectories is highly relevant for human-robot interactions as it allows the anticipation of human motions, fast reaction to those, as well as the recognition of explicit gestures. Further, it allows automated analysis…

In recent years, the crucial importance of metrics in machine learning algorithms has led to an increasing interest for optimizing distance and similarity functions. Most of the state of the art focus on learning Mahalanobis distances…

New geometric and computational analyses of power-weighted shortest-path distances (PWSPDs) are presented. By illuminating the way these metrics balance density and geometry in the underlying data, we clarify their key parameters and…

Representation learning is a fundamental task in machine learning, aiming at uncovering structures from data to facilitate subsequent tasks. However, what is a good representation for planning and reasoning in a stochastic world remains an…