Related papers: Comparing Distributions and Shapes using the Kerne…

The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…

In this paper we present two related, kernel-based Distance Metric Learning (DML) methods. Their respective models non-linearly map data from their original space to an output space, and subsequent distance measurements are performed in the…

Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…

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.…

Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…

Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on the concept of 'distance' or 'similarity'. Before similarities are used for training an actual machine learning model, we…

Graph similarity metrics serve far-ranging purposes across many domains in data science. As graph datasets grow in size, scientists need comparative tools that capture meaningful differences, yet are lightweight and scalable. Graph Relative…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Decision forests induce supervised similarities through the partition structure of their trees. Yet forest proximity computation is still often treated as a quadratic operation in the number of samples, which limits scalability and…

We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and…

This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the…

We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables to directly compare different atomic environments with an arbitrary number of…

Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…

Let P be a distribution with support S. The salient features of S can be quantified with persistent homology, which summarizes topological features of the sublevel sets of the distance function (the distance of any point x to S). Given a…

This work provides theoretical foundations for kernel methods in the hyperspherical context. Specifically, we characterise the native spaces (reproducing kernel Hilbert spaces) and the Sobolev spaces associated with kernels defined over…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

In large scale machine learning and data mining problems with high feature dimensionality, the Euclidean distance between data points can be uninformative, and Distance Metric Learning (DML) is often desired to learn a proper similarity…

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…

Random projections have proven extremely useful in many signal processing and machine learning applications. However, they often require either to store a very large random matrix, or to use a different, structured matrix to reduce the…

In the statistical literature, as well as in artificial intelligence and machine learning, measures of discrepancy between two probability distributions are largely used to develop measures of goodness-of-fit. We concentrate on quadratic…