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Many applications log a large amount of events continuously. Extracting interesting knowledge from logged events is an emerging active research area in data mining. In this context, we propose an approach for mining frequent events and…
We introduce a new metric of match, called Cartesian tree matching, which means that two strings match if they have the same Cartesian trees. Based on Cartesian tree matching, we define single pattern matching for a text of length n and a…
The Fenwick tree is a classical implicit data structure that stores an array in such a way that modifying an element, accessing an element, computing a prefix sum and performing a predecessor search on prefix sums all take logarithmic time.…
Very large time series are increasingly available from an ever wider range of IoT-enabled sensors deployed in different environments. Significant insights can be gained by mining temporal patterns from these time series. Unlike traditional…
The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered…
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
Data mining algorithms are now able to efficiently deal with huge amount of data. Various kinds of patterns may be discovered and may have some great impact on the general development of knowledge. In many domains, end users may want to…
The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…
Mining frequent subgraphs is an area of research where we have a given set of graphs (each graph can be seen as a transaction), and we search for (connected) subgraphs contained in many of these graphs. In this work we will discuss…
In scientific and engineering scenarios, a recurring task is the detection of low-dimensional families of signals or patterns. A classic family of approaches, exemplified by template matching, aims to cover the search space with a dense…
Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…
Rebalancing schemes for dynamic binary search trees are numerous in the literature, where the goal is to maintain trees of low height, either in the worst-case or expected sense. In this paper we study randomized rebalancing schemes for…
For applied intelligence, utility-driven pattern discovery algorithms can identify insightful and useful patterns in databases. However, in these techniques for pattern discovery, the number of patterns can be huge, and the user is often…
Topic models are a popular tool for clustering and analyzing textual data. They allow texts to be classified on the basis of their affiliation to the previously calculated topics. Despite their widespread use in research and application, an…
For an arbitrary, fixed graph (pattern graph), we study the algorithmic complexity of counting homomorphisms, subgraph isomorphisms, and induced subgraph isomorphisms from the pattern graph to $n$-vertex, $d$-degenerate graphs as input.…
Consider a forest that evolves via $link$ operations that make the root of one tree the child of a node in another tree. Intermixed with $link$ operations are $nca$ operations, which return the nearest common ancestor of two given nodes…
Counting the number of occurrences of small connected subgraphs, called temporal motifs, has become a fundamental primitive for the analysis of temporal networks, whose edges are annotated with the time of the event they represent. One of…
A consensus tree is a phylogenetic tree that captures the similarity between a set of conflicting phylogenetic trees. The problem of computing a consensus tree is a major step in phylogenetic tree reconstruction. It also finds applications…
Subspace clustering aims to find groups of similar objects (clusters) that exist in lower dimensional subspaces from a high dimensional dataset. It has a wide range of applications, such as analysing high dimensional sensor data or DNA…