Related papers: On a Generalization of the Average Distance Classi…
A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…
For a fixed, compactly supported probability measure $\mu$ on the $d$-dimensional space $\mathbb{R}^d$, we consider the problem of minimizing the $p^{\mathrm{th}}$-power average distance functional over all compact, connected $\Sigma…
This paper introduces a new (dis)similarity measure for 2D arrays, extending the Average Common Submatrix measure. This is accomplished by: (i) considering the frequency of matching patterns, (ii) restricting the pattern matching to a…
In this paper we consider adaptive sampling's local-feature size, used in surface reconstruction and geometric inference, with respect to an arbitrary landmark set rather than the medial axis and relate it to a path-based adaptive metric on…
In change-point analysis, one aims at finding the locations of abrupt distributional changes (if any) in a sequence of multivariate observations. In this article, we propose some nonparametric methods based on averages of pairwise distances…
Supervised learning is ubiquitous in medical image analysis. In this paper we consider the problem of meta-learning -- predicting which methods will perform well in an unseen classification problem, given previous experience with other…
Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning…
Learning from an imbalanced dataset is a tricky proposition. Because these datasets are biased towards one class, most existing classifiers tend not to perform well on minority class examples. Conventional classifiers usually aim to…
The weighted Euclidean norm $\|x\|_w$ of a vector $x\in \mathbb{R}^d$ with weights $w\in \mathbb{R}^d$ is the Euclidean norm where the contribution of each dimension is scaled by a given weight. Approaches to dimensionality reduction that…
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…
The set of local modes and density ridge lines are important summary characteristics of the data-generating distribution. In this work, we focus on estimating local modes and density ridges from point cloud data in a product space combining…
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…
Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…
We introduce a very general method for high-dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower-dimensional space. In one…
Most classifiers rely on discriminative boundaries that separate instances of each class from everything else. We argue that discriminative boundaries are counter-intuitive as they define semantics by what-they-are-not; and should be…
High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the…
Heteroscedastic classifiers, which learn a multivariate Gaussian distribution over prediction logits, have been shown to perform well on image classification problems with hundreds to thousands of classes. However, compared to standard…
Performance accuracy of the Euclidean Distance Discriminant rule (EDDR) is studied in the high-dimensional asymptotic framework which allows the dimensionality to exceed sample size. Under mild assumptions on the traces of the covariance…
The fundamental task of classification given a limited number of training data samples is considered for physical systems with known parametric statistical models. The standalone learning-based and statistical model-based classifiers face…
In this paper, we extend distance correlation to categorical data with general encodings, such as one-hot encoding for nominal variables and semicircle encoding for ordinal variables. Unlike existing methods, our approach leverages the…