Exploring Communities in Large Profiled Graphs

Given a graph $G$ and a vertex $q\in G$, the community search (CS) problem aims to efficiently find a subgraph of $G$ whose vertices are closely related to $q$. Communities are prevalent in social and biological networks, and can be used in product advertisement and social event recommendation. In this paper, we study profiled community search (PCS), where CS is performed on a profiled graph. This is a graph in which each vertex has labels arranged in a hierarchical manner. Extensive experiments show that PCS can identify communities with themes that are common to their vertices, and is more effective than existing CS approaches. As a naive solution for PCS is highly expensive, we have also developed a tree index, which facilitate efficient and online solutions for PCS

Reductions for Frequency-Based Data Mining Problems

Studying the computational complexity of problems is one of the - if not the - fundamental questions in computer science. Yet, surprisingly little is known about the computational complexity of many central problems in data mining. In this paper we study frequency-based problems and propose a new type of reduction that allows us to compare the complexities of the maximal frequent pattern mining problems in different domains (e.g. graphs or sequences). Our results extend those of Kimelfeld and Kolaitis [ACM TODS, 2014] to a broader range of data mining problems. Our results show that, by allowing constraints in the pattern space, the complexities of many maximal frequent pattern mining problems collapse. These problems include maximal frequent subgraphs in labelled graphs, maximal frequent itemsets, and maximal frequent subsequences with no repetitions. In addition to theoretical interest, our results might yield more efficient algorithms for the studied problems.Comment: This is an extended version of a paper of the same title to appear in the Proceedings of the 17th IEEE International Conference on Data Mining (ICDM'17

Mining frequent closed rooted trees

Many knowledge representation mechanisms are based on tree-like structures, thus symbolizing the fact that certain pieces of information are related in one sense or another. There exists a well-studied process of closure-based data mining in the itemset framework: we consider the extension of this process into trees. We focus mostly on the case where labels on the nodes are nonexistent or unreliable, and discuss algorithms for closurebased mining that only rely on the root of the tree and the link structure. We provide a notion of intersection that leads to a deeper understanding of the notion of support-based closure, in terms of an actual closure operator. We describe combinatorial characterizations and some properties of ordered trees, discuss their applicability to unordered trees, and rely on them to design efficient algorithms for mining frequent closed subtrees both in the ordered and the unordered settings. Empirical validations and comparisons with alternative algorithms are provided.Postprint (author’s final draft

EvoMiner: Frequent Subtree Mining in Phylogenetic Databases

The problem of mining collections of trees to identify common patterns, called frequent subtrees (FSTs), arises often when trying to interpret the results of phylogenetic analysis. FST mining generalizes the well-known maximum agreement subtree problem. Here we present EvoMiner, a new algorithm for mining frequent subtrees in collections of phylogenetic trees. EvoMiner is an Apriori-like level-wise method, which uses a novel phylogeny-specific constant-time candidate generation scheme, an efficient fingerprinting-based technique for downward closure, and a lowest common ancestor based support counting step that requires neither costly subtree operations nor database traversal. Our algorithm achieves speed-ups of up to 100 times or more over Phylominer, the current state-of-the-art algorithm for mining phylogenetic trees. EvoMiner can also work in depth first enumeration mode, to use less memory at the expense of speed. We demonstrate the utility of FST mining as a way to extract meaningful phylogenetic information from collections of trees when compared to maximum agreement subtrees and majority rule trees --- two commonly used approaches in phylogenetic analysis for extracting consensus information from a collection of trees over a common leaf set

Adaptive Learning and Mining for Data Streams and Frequent Patterns

Aquesta tesi està dedicada al disseny d'algorismes de mineria de dades per fluxos de dades que evolucionen en el temps i per l'extracció d'arbres freqüents tancats. Primer ens ocupem de cadascuna d'aquestes tasques per separat i, a continuació, ens ocupem d'elles conjuntament, desenvolupant mètodes de classificació de fluxos de dades que contenen elements que són arbres. En el model de flux de dades, les dades arriben a gran velocitat, i els algorismes que els han de processar tenen limitacions estrictes de temps i espai. En la primera part d'aquesta tesi proposem i mostrem un marc per desenvolupar algorismes que aprenen de forma adaptativa dels fluxos de dades que canvien en el temps. Els nostres mètodes es basen en l'ús de mòduls detectors de canvi i estimadors en els llocs correctes. Proposem ADWIN, un algorisme de finestra lliscant adaptativa, per la detecció de canvi i manteniment d'estadístiques actualitzades, i proposem utilitzar-lo com a caixa negra substituint els comptadors en algorismes inicialment no dissenyats per a dades que varien en el temps. Com ADWIN té garanties teòriques de funcionament, això obre la possibilitat d'ampliar aquestes garanties als algorismes d'aprenentatge i de mineria de dades que l'usin. Provem la nostre metodologia amb diversos mètodes d'aprenentatge com el Naïve Bayes, partició, arbres de decisió i conjunt de classificadors. Construïm un marc experimental per fer mineria amb fluxos de dades que varien en el temps, basat en el programari MOA, similar al programari WEKA, de manera que sigui fàcil pels investigadors de realitzar-hi proves experimentals. Els arbres són grafs acíclics connectats i són estudiats com vincles en molts casos. En la segona part d'aquesta tesi, descrivim un estudi formal dels arbres des del punt de vista de mineria de dades basada en tancats. A més, presentem algorismes eficients per fer tests de subarbres i per fer mineria d'arbres freqüents tancats ordenats i no ordenats. S'inclou una anàlisi de l'extracció de regles d'associació de confiança plena dels conjunts d'arbres tancats, on hem trobat un fenomen interessant: les regles que la seva contrapart proposicional és no trivial, són sempre certes en els arbres a causa de la seva peculiar combinatòria. I finalment, usant aquests resultats en fluxos de dades evolutius i la mineria d'arbres tancats freqüents, hem presentat algorismes d'alt rendiment per fer mineria d'arbres freqüents tancats de manera adaptativa en fluxos de dades que evolucionen en el temps. Introduïm una metodologia general per identificar patrons tancats en un flux de dades, utilitzant la Teoria de Reticles de Galois. Usant aquesta metodologia, desenvolupem un algorisme incremental, un basat en finestra lliscant, i finalment un que troba arbres freqüents tancats de manera adaptativa en fluxos de dades. Finalment usem aquests mètodes per a desenvolupar mètodes de classificació per a fluxos de dades d'arbres.This thesis is devoted to the design of data mining algorithms for evolving data streams and for the extraction of closed frequent trees. First, we deal with each of these tasks separately, and then we deal with them together, developing classification methods for data streams containing items that are trees. In the data stream model, data arrive at high speed, and the algorithms that must process them have very strict constraints of space and time. In the first part of this thesis we propose and illustrate a framework for developing algorithms that can adaptively learn from data streams that change over time. Our methods are based on using change detectors and estimator modules at the right places. We propose an adaptive sliding window algorithm ADWIN for detecting change and keeping updated statistics from a data stream, and use it as a black-box in place or counters or accumulators in algorithms initially not designed for drifting data. Since ADWIN has rigorous performance guarantees, this opens the possibility of extending such guarantees to learning and mining algorithms. We test our methodology with several learning methods as Naïve Bayes, clustering, decision trees and ensemble methods. We build an experimental framework for data stream mining with concept drift, based on the MOA framework, similar to WEKA, so that it will be easy for researchers to run experimental data stream benchmarks. Trees are connected acyclic graphs and they are studied as link-based structures in many cases. In the second part of this thesis, we describe a rather formal study of trees from the point of view of closure-based mining. Moreover, we present efficient algorithms for subtree testing and for mining ordered and unordered frequent closed trees. We include an analysis of the extraction of association rules of full confidence out of the closed sets of trees, and we have found there an interesting phenomenon: rules whose propositional counterpart is nontrivial are, however, always implicitly true in trees due to the peculiar combinatorics of the structures. And finally, using these results on evolving data streams mining and closed frequent tree mining, we present high performance algorithms for mining closed unlabeled rooted trees adaptively from data streams that change over time. We introduce a general methodology to identify closed patterns in a data stream, using Galois Lattice Theory. Using this methodology, we then develop an incremental one, a sliding-window based one, and finally one that mines closed trees adaptively from data streams. We use these methods to develop classification methods for tree data streams.Postprint (published version

PADS: A simple yet effective pattern-aware dynamic search method for fast maximal frequent pattern mining

While frequent pattern mining is fundamental for many data mining tasks, mining maximal frequent patterns efficiently is important in both theory and applications of frequent pattern mining. The fundamental challenge is how to search a large space of item combinations. Most of the existing methods search an enumeration tree of item combinations in a depth-first manner. In this paper, we develop a new technique for more efficient max-pattern mining. Our method is pattern-aware: it uses the patterns already found to schedule its future search so that many search subspaces can be pruned. We present efficient techniques to implement the new approach. As indicated by a systematic empirical study using the benchmark data sets, our new approach outperforms the currently fastest max-pattern mining algorithms FPMax* and LCM2 clearly. The source code and the executable code (on both Windows and Linux platforms) are publicly available at http://www.cs.sfu.ca/~jpei/Software/PADS.zip. © Springer-Verlag London Limited 2008