Related papers: Isometric Words based on Swap and Mismatch Distanc…
The edit distance between strings classically assigns unit cost to every character insertion, deletion, and substitution, whereas the Hamming distance only allows substitutions. In many real-life scenarios, insertions and deletions…
We develop various Ehrenfeucht-Fra\"{\i}ss\'{e} games for distances between metric structures. We study two forms of distances: pseudometrics stemming from mapping spaces onto each other with some form of approximate isomorphism, and…
In this paper we build on earlier observations and theory regarding word length frequency and sequential distribution to develop a mathematical characterization of some of the language features distinguishing isometrically lineated text…
Overlapping frequently occurs in paired texts in natural language processing tasks like text editing and semantic similarity evaluation. Better evaluation of the semantic distance between the overlapped sentences benefits the language…
In this paper, we provide a theoretical understanding of word embedding and its dimensionality. Motivated by the unitary-invariance of word embedding, we propose the Pairwise Inner Product (PIP) loss, a novel metric on the dissimilarity…
An overlap-free (or $\beta$-free) word $w$ over a fixed alphabet $\Sigma$ is extremal if every word obtained from $w$ by inserting a single letter from $\Sigma$ at any position contains an overlap (or a factor of exponent at least $\beta$,…
The concept of edit distance, which dates back to the 1960s in the context of comparing word strings, has since found numerous applications with various adaptations in computer science, computational biology, and applied topology. By…
The structure of all the permutations of a sequence can be represented as a permutohedron, a graph where vertices are permutations and two vertices are linked if a swap of adjacent elements in the permutation of one of the vertices produces…
We define interval spacing as the difference in the order statistics of data over a gap of some width. We derive its density, expected value, and variance for uniform, exponential, and logistic variates. We show that interval spacing is…
This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…
Text-to-pattern distance is a fundamental problem in string matching, where given a pattern of length $m$ and a text of length $n$, over an integer alphabet, we are asked to compute the distance between pattern and the text at every…
Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment is a way to compare sequences, where a giving…
Motivated by the approach of random linear codes, a new distance in the vector space over a finite field is defined as the logarithm of the "surface area" of a Hamming ball with radius being the corresponding Hamming distance. It is named…
Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.
The paper proposes a computationally feasible method for measuring context-sensitive semantic distance between words. The distance is computed by adaptive scaling of a semantic space. In the semantic space, each word in the vocabulary V is…
A key principle in assessing textual similarity is measuring the degree of semantic overlap between two texts by considering the word alignment. Such alignment-based approaches are intuitive and interpretable; however, they are empirically…
Word embeddings are a fixed, distributional representation of the context of words in a corpus learned from word co-occurrences. While word embeddings have proven to have many practical uses in natural language processing tasks, they…
Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has…
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…
A word is quasiperiodic (or coverable) if it can be covered with occurrences of another finite word, called its quasiperiod. A word is multi-scale quasiperiodic (or multi-scale coverable) if it has infinitely many different quasiperiods.…