Related papers: A geometric framework for modelling similarity sea…

A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…

Learning the similarity between images constitutes the foundation for numerous vision tasks. The common paradigm is discriminative metric learning, which seeks an embedding that separates different training classes. However, the main…

In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…

This entry for the SIGSPATIAL Special July 2010 issue on Similarity Searching in Metric Spaces discusses the notion of intrinsic dimensionality of data in the context of similarity search.

We introduce a density-based clustering method called skeleton clustering that can detect clusters in multivariate and even high-dimensional data with irregular shapes. To bypass the curse of dimensionality, we propose surrogate density…

A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric: it can be thought of as an asymmetric metric. The central result of this thesis, developed in Chapter 3, is that a natural correspondence…

We propose a new "bi-metric" framework for designing nearest neighbor data structures. Our framework assumes two dissimilarity functions: a ground-truth metric that is accurate but expensive to compute, and a proxy metric that is cheaper…

Data series are a special type of multidimensional data present in numerous domains, where similarity search is a key operation that has been extensively studied in the data series literature. In parallel, the multidimensional community has…

The similarity between objects is significant in a broad range of areas. While similarity can be measured using off-the-shelf distance functions, they may fail to capture the inherent meaning of similarity, which tends to depend on the…

In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. While…

Similarity search queries in high-dimensional spaces are an important type of queries in many domains such as image processing, machine learning, etc. Since exact similarity search indexing techniques suffer from the well-known curse of…

As datasets grow it becomes infeasible to process them completely with a desired model. For giant datasets, we frame the order in which computation is performed as a decision problem. The order is designed so that partial computations are…

Several problems in stochastic analysis are defined through their geometry, and preserving that geometric structure is essential to generating meaningful predictions. Nevertheless, how to design principled deep learning (DL) models capable…

Graph similarity search algorithms usually leverage the structural properties of a database. Hence, these algorithms are effective only on some structural variations of the data and are ineffective on other forms, which makes them hard to…

Increasingly large data series collections are becoming commonplace across many different domains and applications. A key operation in the analysis of data series collections is similarity search, which has attracted lots of attention and…

In this paper, we propose a novel geometric model fitting method, called Mode-Seeking on Hypergraphs (MSH),to deal with multi-structure data even in the presence of severe outliers. The proposed method formulates geometric model fitting as…

High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states:…

We perform a deeper analysis of an axiomatic approach to the concept of intrinsic dimension of a dataset proposed by us in the IJCNN'07 paper (arXiv:cs/0703125). The main features of our approach are that a high intrinsic dimension of a…

According to the Hughes phenomenon, the major challenges encountered in computations with learning models comes from the scale of complexity, e.g. the so-called curse of dimensionality. There are various approaches for accelerate learning…

The problem of finding an appropriate geometrical/physical index for measuring a degree of inhomogeneity for a given space-time manifold is posed. Interrelations with the problem of understanding the gravitational/informational entropy are…