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

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…

Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…

Graphics play a crucial role in statistical analysis and data mining. This paper describes metrics developed to assist the use of lineups for making inferential statements. Lineups embed the plot of the data among a set of null plots, and…

Clustering is an important part of many modern data analysis pipelines, including network analysis and data retrieval. There are many different clustering algorithms developed by various communities, and it is often not clear which…

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…

Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the…

Trajectories that capture object movement have numerous applications, in which similarity computation between trajectories often plays a key role. Traditionally, the similarity between two trajectories is quantified by means of heuristic…

Deep metric learning employs deep neural networks to embed instances into a metric space such that distances between instances of the same class are small and distances between instances from different classes are large. In most existing…

Learning the undirected graph structure of a Markov network from data is a problem that has received a lot of attention during the last few decades. As a result of the general applicability of the model class, a myriad of methods have been…

In many classification tasks, the set of target classes can be organized into a hierarchy. This structure induces a semantic distance between classes, and can be summarised under the form of a cost matrix, which defines a finite metric on…

A class of distance measures on probabilities -- the integral probability metrics (IPMs) -- is addressed: these include the Wasserstein distance, Dudley metric, and Maximum Mean Discrepancy. IPMs have thus far mostly been used in more…

This paper presents methods to compare high order networks, defined as weighted complete hypergraphs collecting relationship functions between elements of tuples. They can be considered as generalizations of conventional networks where only…

A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…

Mixed-integer linear programming (MILP) is a powerful tool for addressing a wide range of real-world problems, but it lacks a clear structure for comparing instances. A reliable similarity metric could establish meaningful relationships…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

New Matlab functions for network centrality are introduced. Instead of the mean distance, the generalized mean distance is used. If closer relationships are prioritized, this closeness measure is also defined for unconnected graphs. Instead…

Similarity metrics are a core component of many information retrieval and machine learning systems. In this work we propose a method capable of learning a similarity metric from data equipped with a binary relation. By considering only the…

In this paper, a novel statistical metric learning is developed for spectral-spatial classification of the hyperspectral image. First, the standard variance of the samples of each class in each batch is used to decrease the intra-class…

Classical linear metric learning methods have recently been extended along two distinct lines: deep metric learning methods for learning embeddings of the data using neural networks, and Bregman divergence learning approaches for extending…