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Simplicial complexes are a generalization of graphs that model higher-order relations. In this paper, we introduce simplicial patterns -- that we call simplets -- and generalize the task of frequent pattern mining from the realm of graphs…
In this paper we present $LCSk$++: a new metric for measuring the similarity of long strings, and provide an algorithm for its efficient computation. With ever increasing size of strings occuring in practice, e.g. large genomes of plants…
Mining frequent itemsets is at the core of mining association rules, and is by now quite well understood algorithmically. However, most algorithms for mining frequent itemsets assume that the main memory is large enough for the data…
It is generally well agreed that developing a unifying theory is one of the most important issues in Data Mining research. In the last two decades, a great deal of work has been devoted to the algorithmic aspects of the Frequent Itemset…
We consider the general problem of the Longest Common Subsequence (LCS) on weighted sequences. Weighted sequences are an extension of classical strings, where in each position every letter of the alphabet may occur with some probability.…
Graphs are extremely versatile and ubiquitous mathematical structures with potential to model a wide range of domains. For this reason, graph problems have been of interest since the early days of computer science. Some of these problems…
Strings form a fundamental data type in computer systems. String searching has been extensively studied since the inception of computer science. Increasingly many applications have to deal with imprecise strings or strings with fuzzy…
We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in…
Longest Increasing Subsequence (LIS) is a fundamental statistic of a sequence, and has been studied for decades. While the LIS of a sequence of length $n$ can be computed exactly in time $O(n\log n)$, the complexity of estimating the…
Non-parametric entropy estimation on sequential data is a fundamental tool in signal processing, capturing information flow within or between processes to measure predictability, redundancy, or similarity. Methods based on longest common…
The {\em shortest common superstring} and the {\em shortest common supersequence} are two well studied problems having a wide range of applications. In this paper we consider both problems with resource constraints, denoted as the…
As with the development of the IT technologies, the amount of accumulated data is also increasing. Thus the role of data mining comes into picture. Association rule mining becomes one of the significant responsibilities of descriptive…
We study the problem of frequent itemset mining in domains where data is not recorded in a conventional database but only exists in human knowledge. We provide examples of such scenarios, and present a crowdsourcing model for them. The…
In this work, we consider a variant of the classical Longest Common Subsequence problem called Doubly-Constrained Longest Common Subsequence (DC-LCS). Given two strings s1 and s2 over an alphabet A, a set C_s of strings, and a function Co…
Most of the fastest-growing string collections today are repetitive, that is, most of the constituent documents are similar to many others. As these collections keep growing, a key approach to handling them is to exploit their…
Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…
Data mining has been widely recognized as a powerful tool to explore added value from large-scale databases. Finding frequent item sets in databases is a crucial in data mining process of extracting association rules. Many algorithms were…
Biclustering techniques have been widely used to identify homogeneous subgroups within large data matrices, such as subsets of genes similarly expressed across subsets of patients. Mining a max-sum sub-matrix is a related but distinct…
Suppose we want to seek the longest common subsequences (LCSs) of two strings as informative patterns that explain the relationship between the strings. The dynamic programming algorithm gives us a table from which all LCSs can be extracted…
The process of data mining produces various patterns from a given data source. The most recognized data mining tasks are the process of discovering frequent itemsets, frequent sequential patterns, frequent sequential rules and frequent…