Related papers: Classifying token frequencies using angular Minkow…

Imitation learning algorithms have been interpreted as variants of divergence minimization problems. The ability to compare occupancy measures between experts and learners is crucial in their effectiveness in learning from demonstrations.…

For pattern recognition like image recognition, it has become clear that each machine-learning dictionary data actually became data in probability space belonging to Euclidean space. However, the distances in the Euclidean space and the…

In this paper, we generalize the Minkowski distance by defining a new distance function in n-dimensional space, and we show that this function determines also a metric family as the Minkowski distance. Then, we consider three special cases…

The problem of nearest neighbor condensing has enjoyed a long history of study, both in its theoretical and practical aspects. In this paper, we introduce the problem of weighted distance nearest neighbor condensing, where one assigns…

The "maximum similarity correlation" definition introduced in this study is motivated by the seminal work of Szekely et al on "distance covariance" (Ann. Statist. 2007, 35: 2769-2794; Ann. Appl. Stat. 2009, 3: 1236-1265). Instead of using…

Approximate spectral clustering (ASC) was developed to overcome heavy computational demands of spectral clustering (SC). It maintains SC ability in predicting non-convex clusters. Since it involves a preprocessing step, ASC defines new…

In the evolving landscape of sixth-generation (6G) wireless networks, which demand ultra high data rates, this study introduces the concept of super constellation communications. Also, we present super amplitude phase shift keying (SAPSK),…

In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…

We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of the…

Evaluation plays a significant role in modern natural language processing. Most modern NLP benchmarks consist of arbitrary sets of tasks that neither guarantee any generalization potential for the model once applied outside the test set nor…

Similarity search is a fundamental problem for many data analysis techniques. Many efficient search techniques rely on the triangle inequality of metrics, which allows pruning parts of the search space based on transitive bounds on…

In this paper, we tackle the problem of measuring similarity among graphs that represent real objects with noisy data. To account for noise, we relax the definition of similarity using the maximum weighted co-$k$-plex relaxation method,…

Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for…

Deep Learning performs well when training data densely covers the experience space. For complex problems this makes data collection prohibitively expensive. We propose to intelligently select samples when constructing data sets in order to…

We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…

Motivated by the Bures distance, we introduce a new family of distances, \emph{relative translation invariant Wasserstein distances}, denoted by $RW_p$, as an extension of the classical Wasserstein distances $W_p$ for $p \in [1, +\infty)$.…

Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data structures. In real world applications, such an assumption of…

The Universal Similarity Metric (USM) has been demonstrated to give practically useful measures of "similarity" between sequence data. Here we have used the USM as an alternative distance metric in a K-Nearest Neighbours (K-NN) learner to…

We present a definition of the distance between probability distributions. Our definition is based on the $L_1$ norm on space of probability measures. We compare our distance with the well-known Kullback-Leibler divergence and with the…

Window profiles of amino acids in protein sequences are taken as a description of the amino acid environment. The relative entropy or Kullback-Leibler distance derived from profiles is used as a measure of dissimilarity for comparison of…