Related papers: Procrustes-based distances for exploring between-m…
Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big…
Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks…
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…
The human visual system is able to recognize objects despite transformations that can drastically alter their appearance. To this end, much effort has been devoted to the invariance properties of recognition systems. Invariance can be…
In machine learning, observation features are measured in a metric space to obtain their distance function for optimization. Given similar features that are statistically sufficient as a population, a statistical distance between two…
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-based regression model, as a nonparametric multivariate method, has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic…
This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the…
Tree shape statistics quantify some aspect of the shape of a phylogenetic tree. They are commonly used to compare reconstructed trees to evolutionary models and to find evidence of tree reconstruction bias. Historically, to find a useful…
The distance matrix of a dataset $X$ of $n$ points with respect to a distance function $f$ represents all pairwise distances between points in $X$ induced by $f$. Due to their wide applicability, distance matrices and related families of…
The constrained orthogonal Procrustes problem is the least-squares problem that calls for a rotation matrix that optimally aligns two corresponding sets of points in d-dimensional Euclidean space. This problem generalizes to the so-called…
A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio. At each iteration, a smaller trace ratio problem is…
Distance metric learning has attracted a lot of interest for solving machine learning and pattern recognition problems over the last decades. In this work we present a simple approach based on concepts from statistical physics to learn…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
Tractograms are mathematical representations of the main paths of axons within the white matter of the brain, from diffusion MRI data. Such representations are in the form of polylines, called streamlines, and one streamline approximates…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the…
This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…
We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to…
Material microstructures are traditionally compared using sets of statistical measures that are incomplete, e.g., two visually distinct microstructures can have identical grain size distributions and phase fractions. While this is not a…