Frequent itemset mining (FIM) is one of the core problems in the field of Data Mining and occupies a central place in its literature. One equivalent form of FIM can be stated as follows: given a rectangular data matrix with binary entries, find every submatrix of 1s having a minimum number of columns. This paper presents a theoretical analysis of several statistical questions related to this pr...

Two algorithmic techniques for specifying the existence of a k×k submatrix with elements 0,±1 in a skew and symmetric conference matrix of order n are described. This specification is achieved using an appropriate computer algebra system.

In this literature, the symmetric inverse generalized eigenvalue problem with submatrix constraints and its corresponding optimal approximation problem are studied. A necessary and sufficient condition for solvability is derived, and when solvable, the general solutions are presented.

We consider a number of generalizations of the β-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements over matrix or submatrix indices.

Extracting k-order maximal-sum principal submatrix from an n-order real matrix is a typical combinatorial optimization problem and NP-hard problem. To improve the computational efficiency of solving this problem, we, in paper, propose accelerated algorithm with row-by-row updates, called fusion row update algorithm, which works by reducing number addition operations for elements. The new applie...

Bogdanov and Lee suggested a homomorphic public-key encryption scheme based on error correcting codes. The underlying public code is a modified Reed-Solomon code obtained from inserting a zero submatrix in the Vandermonde generating matrix defining it. The columns that define this submatrix are kept secret and form a set L. We give here a distinguisher that detects if one or several columns bel...

Order-Preserving SubMatrix (OPSM) has been accepted as a significant tool in modelling biologically meaningful subspace cluster, to discover the general tendency of gene expressions across a subset of conditions. Existing OPSM processing tools focus on giving a or some batch mining techniques, and are time-consuming and do not consider to support OPSM queries. To address the problems, the paper...