相关论文: Algorithmic coincidence classification of mesh pat…

An adjacent $q$-cycle is a natural generalization of an adjacent transposition. We show that the number of adjacent $q$-cycles in a permutation maps to the sum of occurrences of two mesh patterns under Foata's fundamental transformation. As…

In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…

We explore how the asymptotic structure of a random permutation of $[n]$ with $m$ inversions evolves, as $m$ increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. The…

We review how the monotone pattern compares to other patterns in terms of enumerative results on pattern avoiding permutations. We consider three natural definitions of pattern avoidance, give an overview of classic and recent formulas, and…

Pattern comparison represents a fundamental and crucial aspect of scientific modeling, artificial intelligence, and pattern recognition. Three main approaches have typically been applied for pattern comparison: (i) distances; (ii)…

In this paper, we introduce novel characterizations of the classical concept of majorization in terms of upper triangular (resp., lower triangular) row-stochastic matrices, and in terms of sequences of linear transforms on vectors. We used…

We count the number of occurrences of restricted patterns of length 3 in permutations with respect to length and the number of cycles. The main tool is a bijection between permutations in standard cycle form and weighted Motzkin paths.

Permutation resemblance measures the distance of a function from being a permutation. Here we show how to determine the permutation resemblance through linear integer programming techniques. We also present an algorithm for constructing…

Large-scale Hierarchical Classification (HC) involves datasets consisting of thousands of classes and millions of training instances with high-dimensional features posing several big data challenges. Feature selection that aims to select…

We study a family of equivalence relations on $S_n$, the group of permutations on $n$ letters, created in a manner similar to that of the Knuth relation and the forgotten relation. For our purposes, two permutations are in the same…

In this paper we provide a novel mathematical optimization based methodology to perturb the features of a given observation to be re-classified, by a tree ensemble classification rule, to a certain desired class. The method is based on…

We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution,…

We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations…

The article considers classification task of fractal time series by the meta algorithms based on decision trees. Binomial multiplicative stochastic cascades are used as input time series. Comparative analysis of the classification…

Permutation matrices play an important role in understand the structure of magic squares. In this work, we use a class of symmetric permutation matrices than can be used to categorize magic squares. Many magic squares with a high degree of…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

We present a novel method to perform multi-class pattern classification with neural networks and test it on a challenging 3D hand gesture recognition problem. Our method consists of a standard one-against-all (OAA) classification, followed…

The structure of three pattern classes Av(2143, 4321), Av(2143, 4312) and Av(1324, 4312) is determined using the machinery of monotone grid classes. This allows the permutations in these classes to be described in terms of simple diagrams…

In this paper, we reveal an intriguing relationship between two seemingly unrelated notions: letter graphs and geometric grid classes of permutations. An important property common for both of them is well-quasi-orderability, implying, in a…

A consecutive pattern in a permutation $\pi$ is another permutation $\sigma$ determined by the relative order of a subsequence of contiguous entries of $\pi$. Traditional notions such as descents, runs and peaks can be viewed as particular…