Related papers: A Triangle Inequality for Cosine Similarity

Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and…

Cosine similarity of contextual embeddings is used in many NLP tasks (e.g., QA, IR, MT) and metrics (e.g., BERTScore). Here, we uncover systematic ways in which word similarities estimated by cosine over BERT embeddings are understated and…

Similarity search is the problem of finding in a collection of objects those that are similar to a given query object. It is a fundamental problem in modern applications and the objects considered may be as diverse as locations in space,…

Multimodal alignment is critical for bridging the semantic gap in information retrieval. However, traditional pairwise strategies introduce a geometric blind spot: while they align anchor modalities (e.g., text) with others, they lack…

Two new algorithms are described for matching two dimensional coordinate lists of point sources that are signifcantly faster than previous methods. By matching rarely occurring triangles (or more complex shapes) in the two lists, and by…

In derivative-free optimization, the cosine measure is a value that often arises in the convergence analysis of direct search methods. Given the increasing interest in high-dimensional derivative-free optimization problems, it is valuable…

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

Similarity search, the task of identifying objects most similar to a given query object under a specific metric, has gathered significant attention due to its practical applications. However, the absence of coordinate information to…

Metric learning aims to construct an embedding where two extracted features corresponding to the same identity are likely to be closer than features from different identities. This paper presents a method for learning such a feature space…

This paper presents a deep nonlinear metric learning framework for data visualization on an image dataset. We propose the Triangular Similarity and prove its equivalence to the Cosine Similarity in measuring a data pair. Based on this novel…

Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…

An important problem in geometric computing is defining and computing similarity between two geometric shapes, e.g. point sets, curves and surfaces, etc. Important geometric and topological information of many shapes can be captured by…

Cross-modal similarity search is a problem about designing a search system supporting querying across content modalities, e.g., using an image to search for texts or using a text to search for images. This paper presents a compact coding…

A common approach to implementing similarity search applications is the usage of distance functions, where small distances indicate high similarity. In the case of metric distance functions, metric index structures can be used to accelerate…

One of the important factors that make a search engine fast and accurate is a concise and duplicate free index. In order to remove duplicate and near-duplicate documents from the index, a search engine needs a swift and reliable duplicate…

An ultrametric space or infinity-metric space is defined by a dissimilarity function that satisfies a strong triangle inequality in which every side of a triangle is not larger than the larger of the other two. We show that search in…

Metric search is concerned with the efficient evaluation of queries in metric spaces. In general,a large space of objects is arranged in such a way that, when a further object is presented as a query, those objects most similar to the query…

The generation and collection of big data series are becoming an integral part of many emerging applications in sciences, IoT, finance, and web applications among several others. The terabyte-scale of data series has motivated recent…

Similarity search retrieves the nearest neighbors of a query vector from a dataset of high-dimensional vectors. As the size of the dataset grows, the cost of performing the distance computations needed to implement a query can become…

Code search is vital in the maintenance and extension of software systems. Past works have used separate language models for the natural language and programming language artifacts on models with multiple encoders and different loss…