Related papers: Distance approximation using Isolation Forests
In this work we define a novel edit distance for trees considered with some abstract weights on the edges. The metric is driven by the idea of considering trees as topological summaries in the context of persistence and topological data…
Anomaly Detection is an unsupervised learning task aimed at detecting anomalous behaviours with respect to historical data. In particular, multivariate Anomaly Detection has an important role in many applications thanks to the capability of…
We survey the emerging area of compression-based, parameter-free, similarity distance measures useful in data-mining, pattern recognition, learning and automatic semantics extraction. Given a family of distances on a set of objects, a…
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…
Understanding the mutational history of tumor cells is a critical endeavor in unraveling the mechanisms underlying cancer. Since the modeling of tumor cell evolution employs labeled trees, researchers are motivated to develop different…
Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths…
In this paper, we propose a new method for determining shared features of and measuring the distance between data sets or point clouds. Our approach uses the joint factorization of two data matrices $X_1,X_2$ into non-negative matrices $X_1…
Differential privacy is a widely studied notion of privacy for various models of computation. Technically, it is based on measuring differences between probability distributions. We study $\epsilon,\delta$-differential privacy in the…
Distance measurement is crucial to astronomy. Here we suggest a new conceptual method to measure the distance by using a local instrument. By engaging the double-slit interference and by considering the phase information of the light, the…
First we consider pair-wise distances for literal objects consisting of finite binary files. These files are taken to contain all of their meaning, like genomes or books. The distances are based on compression of the objects concerned,…
We propose a family of graph structural indices related to the Matrix-forest theorem. The properties of the basic index that expresses the mutual connectivity of two vertices are studied in detail. The derivative indices that measure…
We consider the problem of allocating samples to a finite set of discrete distributions in order to learn them uniformly well in terms of four common distance measures: $\ell_2^2$, $\ell_1$, $f$-divergence, and separation distance. To…
Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
We present the first review of methods to overapproximate the set of reachable states of linear time-invariant systems subject to uncertain initial states and input signals for short time horizons. These methods are fundamental to…
In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…
In the $L_0$ Fitting Tree Metrics problem, we are given all pairwise distances among the elements of a set $V$ and our output is a tree metric on $V$. The goal is to minimize the number of pairwise distance disagreements between the input…
Exploratory data analysis is crucial for developing and understanding classification models from high-dimensional datasets. We explore the utility of a new unsupervised tree ensemble called uncharted forest for visualizing class…
Phylogenetic trees are a central tool in understanding evolution. They are typically inferred from sequence data, and capture evolutionary relationships through time. It is essential to be able to compare trees from different data sources…
Unobtrusive monitoring of distances between people indoors is a useful tool in the fight against pandemics. A natural resource to accomplish this are surveillance cameras. Unlike previous distance estimation methods, we use a single,…