Related papers: A new class of metrics for learning on real-valued…
The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This…
Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…
We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…
In this paper, we present a novel two-stage metric learning algorithm. We first map each learning instance to a probability distribution by computing its similarities to a set of fixed anchor points. Then, we define the distance in the…
We propose a family of near-metrics based on local graph diffusion to capture similarity for a wide class of data sets. These quasi-metametrics, as their names suggest, dispense with one or two standard axioms of metric spaces, specifically…
In data analysis, there is a strong demand for graph metrics that differ from the classical shortest path and resistance distances. Recently, several new classes of graph metrics have been proposed. This paper presents some of them…
The shortest-path, commute time, and diffusion distances on undirected graphs have been widely employed in applications such as dimensionality reduction, link prediction, and trip planning. Increasingly, there is interest in using…
The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts…
Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…
Studies on various facets of pattern classification is often imperative while working with multi-dimensional samples pertaining to diverse application scenarios. In this notion, weighted dimension-based distance measure has been one of the…
Acyclic digraphs arise in many natural and artificial processes. Among the broader set, dynamic citation networks represent a substantively important form of acyclic digraphs. For example, the study of such networks includes the spread of…
There are many distance-based methods for classification and clustering, and for data with a high number of dimensions and a lower number of observations, processing distances is computationally advantageous compared to the raw data matrix.…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
We propose a new method for local distance metric learning based on sample similarity as side information. These local metrics, which utilize conical combinations of metric weight matrices, are learned from the pooled spatial…
Although the notion of task similarity is potentially interesting in a wide range of areas such as curriculum learning or automated planning, it has mostly been tied to transfer learning. Transfer is based on the idea of reusing the…
Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…
Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…
Motivated by information geometry, a distance function on the space of stochastic matrices is advocated. Starting with sequences of Markov chains the Bhattacharyya angle is advocated as the natural tool for comparing both short and long…