Related papers: Metric Comparisons of Relations
This paper studies the properties of a new lower bound for the natural pseudo-distance. The natural pseudo-distance is a dissimilarity measure between shapes, where a shape is viewed as a topological space endowed with a real-valued…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic…
Over the recent years, there has been a growing interest in developing new research evaluation methods that could go beyond the traditional citation-based metrics. This interest is motivated on one side by the wider availability or even…
We propose a class of semimetrics for preference relations any one of which is an alternative to the classical Kemeny-Snell-Bogart metric. (We take a fairly general viewpoint about what constitutes a preference relation, allowing for any…
Measuring inter-dataset similarity is an important task in machine learning and data mining with various use cases and applications. Existing methods for measuring inter-dataset similarity are computationally expensive, limited, or…
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…
We consider pairs of a non-empty compact connected and locally connected Hausdorff space and a real-valued continuous function. Our aim is to measure the difference between this kind of the pairs. In this notes we introduce new…
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
We develop a pseudo-metric analogue of bisimulation for generalized semi-Markov processes. The kernel of this pseudo-metric corresponds to bisimulation; thus we have extended bisimulation for continuous-time probabilistic processes to a…
Suplementary algoritm for optimizing technological parameters of soft magnetic compozities has been derived on the base of topological structure of the power loss characteristics. In optimization processes of magnitudes obeying scaling it…
In this technical note, we introduce a novel approach to studying consensus of continuous-time nonlinear systems with varying topology based on Hilbert metric. We demonstrate that this metric offers significant flexibility in analyzing…
In big data times, massive datasets often carry different relationships among the same group of nodes, analyzing on these heterogeneous relationships may give us a window to peek the essential relationships among nodes. In this paper, first…
If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below…
In any setting in which observable properties have a quantitative flavour, it is natural to compare computational objects by way of \emph{metrics} rather than equivalences or partial orders. This holds, in particular, for probabilistic…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
The notion of rough set captures indiscernibility of elements in a set. But, in many real life situations, an information system establishes the relation between different universes. This gave the extension of rough set on single universal…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…
Existing discourse formalisms use different taxonomies of discourse relations, which require expert knowledge to understand, posing a challenge for annotation and automatic classification. We show that discourse relations can be effectively…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…