Related papers: A weighted angle distance on strings
Using the technique of the metrization theorem of uniformities with countable bases, in this note we provide, test and compare an explicit algorithm to produce a metric $d(x,y)$ between the vertices $x$ and $y$ of an affinity weighted…
This paper presents methods to compare high order networks, defined as weighted complete hypergraphs collecting relationship functions between elements of tuples. They can be considered as generalizations of conventional networks where only…
Hidden structural patterns in written texts have been subject of considerable research in the last decades. In particular, mapping a text into a time series of sentence lengths is a natural way to investigate text structure. Typically,…
Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…
We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of…
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…
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 introduce and study three new measures for efficient discriminative comparison of phylogenetic trees. The NNI navigation dissimilarity $d_{nav}$ counts the steps along a "combing" of the Nearest Neighbor Interchange (NNI)…
We study optimization problems in a metric space $(\mathcal{X},d)$ where we can compute distances in two ways: via a ''strong'' oracle that returns exact distances $d(x,y)$, and a ''weak'' oracle that returns distances $\tilde{d}(x,y)$…
This paper deals with the complexity of strings, which play an important role in biology (nucleotid sequences), information theory and computer science. The d-complexity of a string is defined as the number of its distinct d-substrings…
We hereby present a solution to a semantic textual similarity (STS) problem in which it is necessary to match two sentences containing, as the only distinguishing factor, highly specific information (such as names, addresses, identification…
In order to conduct analyses of networked systems where connections between individuals take on a range of values - counts, continuous strengths or ordinal rankings - a common technique is to dichotomize the data according to their…
In scientific visualization, scalar fields are often compared through edit distances between their merge trees. Typical tasks include ensemble analysis, feature tracking and symmetry or periodicity detection. Tree edit distances represent…
DBSCAN and OPTICS are powerful algorithms for identifying clusters of points in domains where few assumptions can be made about the structure of the data. In this paper, we leverage these strengths and introduce a new algorithm, LINSCAN,…
We are given a set of elements in a metric space. The distribution of the elements is arbitrary, possibly adversarial. Can we weigh the elements in a way that is resistant to such (adversarial) manipulations? This problem arises in various…
We study the properties of several proximity measures for the vertices of weighted multigraphs and multidigraphs. Unlike the classical distance for the vertices of connected graphs, these proximity measures are applicable to weighted…
With the development of multimedia time, one sample can always be described from multiple views which contain compatible and complementary information. Most algorithms cannot take information from multiple views into considerations and fail…
Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely applicable and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in…
Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…
We develop an operator formalism to compute scattering amplitudes of arbitrary bosonic string states in the background of many D-branes. Specifically, we construct a suitable boundary state which we use to saturate the multi-Reggeon vertex…