Related papers: A Triangle Inequality for Cosine Similarity
In this paper we introduce and study three new measures for efficient discriminative comparison of phylogenetic trees. The NNI navigation dissimilarity $d_{nav}$ counts the steps along a "combing" of the Nearest Neighbor Interchange (NNI)…
We show that there is no $(1+\eps)$-approximation algorithm for the problem of covering points in the plane by minimum number of fat triangles of similar size (with the minimum angle of the triangles being close to 45 degrees). Here, the…
Many emerging use cases of data mining and machine learning operate on large datasets with data from heterogeneous sources, specifically with both sparse and dense components. For example, dense deep neural network embedding vectors are…
Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we…
Edit distance similarity search, also called approximate pattern matching, is a fundamental problem with widespread database applications. The goal of the problem is to preprocess $n$ strings of length $d$, to quickly answer queries $q$ of…
Similarity search is an important function in many applications, which usually focuses on measuring the similarity between objects with the same type. However, in many scenarios, we need to measure the relatedness between objects with…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
Hash coding has been widely used in the approximate nearest neighbor search for large-scale image retrieval. Recently, many deep hashing methods have been proposed and shown largely improved performance over traditional…
Searching topological similarity between a pair of shapes or data is an important problem in data analysis and visualization. The problem of computing similarity measures using scalar topology has been studied extensively and proven useful…
With the ever-increasing quantity and variety of data worldwide, the Web has become a rich repository of mathematical formulae. This necessitates the creation of robust and scalable systems for Mathematical Information Retrieval, where…
Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…
Different machine learning models can represent the same underlying concept in different ways. This variability is particularly valuable for in-the-wild multimodal retrieval, where the objective is to identify the corresponding…
We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads…
Cycles are ubiquitous in various networks such as social, biological, and technological systems, where they play a significant functional and dynamical role. This paper proposes a node similarity measure based on minimal simple cycles,…
Monte Carlo Tree Search is a popular method for solving decision making problems. Faster implementations allow for more simulations within the same wall clock time, directly improving search performance. To this end, we present an…
Sequence classification algorithms, such as SVM, require a definition of distance (similarity) measure between two sequences. A commonly used notion of similarity is the number of matches between $k$-mers ($k$-length subsequences) in the…
Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…
We study the problem of finding the $k$ most similar trajectories to a given query trajectory. Our work is inspired by the work of Grossi et al. [6] that considers trajectories as walks in a graph. Each visited vertex is accompanied by a…
We present an extension of Monte Carlo Tree Search (MCTS) that strongly increases its efficiency for trees with asymmetry and/or loops. Asymmetric termination of search trees introduces a type of uncertainty for which the standard upper…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…