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

Reverse-Safe Data Structures for Text Indexing

We introduce the notion of reverse-safe data structures. These are data structures that prevent the reconstruction of the data they encode (i.e., they cannot be easily reversed). A data structure D is called z-reverse-safe when there exist at least z datasets with the same set of answers as the ones stored by D. The main challenge is to ensure that D stores as many answers to useful queries as possible, is constructed efficiently, and has size close to the size of the original dataset it encodes. Given a text of length n and an integer z, we propose an algorithm which constructs a z-reverse-safe data structure that has size O(n) and answers pattern matching queries of length at most d optimally, where d is maximal for any such z-reverse-safe data structure. The construction algorithm takes O(n ω log d) time, where ω is the matrix multiplication exponent. We show that, despite the n ω factor, our engineered implementation takes only a few minutes to finish for million-letter texts. We further show that plugging our method in data analysis applications gives insignificant or no data utility loss. Finally, we show how our technique can be extended to support applications under a realistic adversary model

Motif counting beyond five nodes

Counting graphlets is a well-studied problem in graph mining and social network analysis. Recently, several papers explored very simple and natural algorithms based on Monte Carlo sampling of Markov Chains (MC), and reported encouraging results. We show, perhaps surprisingly, that such algorithms are outperformed by color coding (CC) [2], a sophisticated algorithmic technique that we extend to the case of graphlet sampling and for which we prove strong statistical guarantees. Our computational experiments on graphs with millions of nodes show CC to be more accurate than MC; furthermore, we formally show that the mixing time of the MC approach is too high in general, even when the input graph has high conductance. All this comes at a price however. While MC is very efficient in terms of space, CC’s memory requirements become demanding when the size of the input graph and that of the graphlets grow. And yet, our experiments show that CC can push the limits of the state-of-the-art, both in terms of the size of the input graph and of that of the graphlets

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

Temporalized logics and automata for time granularity

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym: TPLP Category: Paper for Special Issue (Verification and Computational Logic) Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September 200

Graph-based Modelling of Concurrent Sequential Patterns

Structural relation patterns have been introduced recently to extend the search for complex patterns often hidden behind large sequences of data. This has motivated a novel approach to sequential patterns post-processing and a corresponding data mining method was proposed for Concurrent Sequential Patterns (ConSP). This article refines the approach in the context of ConSP modelling, where a companion graph-based model is devised as an extension of previous work. Two new modelling methods are presented here together with a construction algorithm, to complete the transformation of concurrent sequential patterns to a ConSP-Graph representation. Customer orders data is used to demonstrate the effectiveness of ConSP mining while synthetic sample data highlights the strength of the modelling technique, illuminating the theories developed