Compositional Mining of Multi-Relational Biological Datasets

High-throughput biological screens are yielding ever-growing streams of information about multiple aspects of cellular activity. As more and more categories of datasets come online, there is a corresponding multitude of ways in which inferences can be chained across them, motivating the need for compositional data mining algorithms. In this paper, we argue that such compositional data mining can be effectively realized by functionally cascading redescription mining and biclustering algorithms as primitives. Both these primitives mirror shifts of vocabulary that can be composed in arbitrary ways to create rich chains of inferences. Given a relational database and its schema, we show how the schema can be automatically compiled into a compositional data mining program, and how different domains in the schema can be related through logical sequences of biclustering and redescription invocations. This feature allows us to rapidly prototype new data mining applications, yielding greater understanding of scientific datasets. We describe two applications of compositional data mining: (i) matching terms across categories of the Gene Ontology and (ii) understanding the molecular mechanisms underlying stress response in human cells

SQL Query Completion for Data Exploration

Within the big data tsunami, relational databases and SQL are still there and remain mandatory in most of cases for accessing data. On the one hand, SQL is easy-to-use by non specialists and allows to identify pertinent initial data at the very beginning of the data exploration process. On the other hand, it is not always so easy to formulate SQL queries: nowadays, it is more and more frequent to have several databases available for one application domain, some of them with hundreds of tables and/or attributes. Identifying the pertinent conditions to select the desired data, or even identifying relevant attributes is far from trivial. To make it easier to write SQL queries, we propose the notion of SQL query completion: given a query, it suggests additional conditions to be added to its WHERE clause. This completion is semantic, as it relies on the data from the database, unlike current completion tools that are mostly syntactic. Since the process can be repeated over and over again -- until the data analyst reaches her data of interest --, SQL query completion facilitates the exploration of databases. SQL query completion has been implemented in a SQL editor on top of a database management system. For the evaluation, two questions need to be studied: first, does the completion speed up the writing of SQL queries? Second , is the completion easily adopted by users? A thorough experiment has been conducted on a group of 70 computer science students divided in two groups (one with the completion and the other one without) to answer those questions. The results are positive and very promising

Non-parametric Methods for Correlation Analysis in Multivariate Data with Applications in Data Mining

In this thesis, we develop novel methods for correlation analysis in multivariate data, with a special focus on mining correlated subspaces. Our methods handle major open challenges arisen when combining correlation analysis with subspace mining. Besides traditional correlation analysis, we explore interaction-preserving discretization of multivariate data and causality analysis. We conduct experiments on a variety of real-world data sets. The results validate the benefits of our methods

Mining XML Documents

XML documents are becoming ubiquitous because of their rich and flexible format that can be used for a variety of applications. Giving the increasing size of XML collections as information sources, mining techniques that traditionally exist for text collections or databases need to be adapted and new methods to be invented to exploit the particular structure of XML documents. Basically XML documents can be seen as trees, which are well known to be complex structures. This chapter describes various ways of using and simplifying this tree structure to model documents and support efficient mining algorithms. We focus on three mining tasks: classification and clustering which are standard for text collections; discovering of frequent tree structure which is especially important for heterogeneous collection. This chapter presents some recent approaches and algorithms to support these tasks together with experimental evaluation on a variety of large XML collections

Information retrieval and mining in high dimensional databases

This dissertation is composed of two parts. In the first part, we present a framework for finding information (more precisely, active patterns) in three dimensional (3D) graphs. Each node in a graph is an undecoraposable or atomic unit and has a label. Edges are links between the atomic units. Patterns are rigid substructures that may occur in a graph after allowing for an arbitrary number of whole-structure rotations and translations as well as a small number (specified by the user) of edit operations in the patterns or in the graph. (When a pattern appears in a graph only after the graph has been modified, we call that appearance approximate occurrence. ) The edit operations include relabeling a node, deleting a node and inserting a node. The proposed method is based on the geometric hashing technique, which hashes node-triplets of the graphs into a 3D table and compresses the label-triplets in the table. To demonstrate the utility of our algorithms, we discuss two applications of them in scientific data mining. First, we apply the method to locating frequently occurring motifs in two families of proteins pertaining to RNA-directed DNA Polymerase and Thymidylate Synthase, and use the motifs to classify the proteins. Then we apply the method to clustering chemical compounds pertaining to aromatic, bicyclicalkanes and photosynthesis. Experimental results indicate the good performance of our algorithms and high recall and precision rates for both classification and clustering. We also extend our algorithms for processing a class of similarity queries in databases of 3D graphs. In the second part of the dissertation, we present an index structure, called MetricMap, that takes a set of objects and a distance metric and then maps those objects to a k-dimensional pseudo-Euclidean space in such a way that the distances among objects are approximately preserved. Our approach employs sampling and the calculation of eigenvalues and eigenvectors. The index structure is a useful tool for clustering and visualization in data intensive applications, because it replaces expensive distance calculations by sum-of-square calculations. This can make clustering in large databases with expensive distance metrics practical. We compare the index structure with another data mining index structure, FastMap, proposed by Faloutsos and Lin, according to two criteria: relative error and clustering accuracy. For relative error, we show that (i) FastMap gives a lower relative error than MetrieMap for Euclidean distances, (ii) MetricMap gives a lower relative error than Fast Map for non-Euclidean distances (i.e., general distance metrics), and (iii) combining the two reduces the error yet further. A similar result is obtained when comparing the accuracy of clustering. These results hold for different data sizes. The main qualitative conclusion is that these two index structures capture complenleiltary information about distance metrics and therefore can be used together to great benefit. The net effect is that multi-day computations can be done in minutes. We have implemented the proposed algorithms and the MetricMap index structure into a toolkit. This toolkit will be useful for data mining, visualization, and approximate retrieval in scientific, multimedia and high dimensional databases

The Minimum Description Length Principle for Pattern Mining: A Survey

This is about the Minimum Description Length (MDL) principle applied to pattern mining. The length of this description is kept to the minimum. Mining patterns is a core task in data analysis and, beyond issues of efficient enumeration, the selection of patterns constitutes a major challenge. The MDL principle, a model selection method grounded in information theory, has been applied to pattern mining with the aim to obtain compact high-quality sets of patterns. After giving an outline of relevant concepts from information theory and coding, as well as of work on the theory behind the MDL and similar principles, we review MDL-based methods for mining various types of data and patterns. Finally, we open a discussion on some issues regarding these methods, and highlight currently active related data analysis problems

Algorithms for finding orders and analyzing sets of chains

Rankings of items are a useful concept in a variety of applications, such as clickstream analysis, some voting methods, bioinformatics, and other fields of science such as paleontology. This thesis addresses two problems related to such data. The first problem is about finding orders, while the second one is about analyzing sets of orders. We address two different tasks in the problem of finding orders. We can find orders either by computing an aggregate of a set of known orders, or by constructing an order for a previously unordered data set. For the first task we show that bucket orders, a subclass of partial orders, are a useful structure for summarizing sets of orders. We formulate an optimization problem for finding such partial orders, show that it is NP-hard, and give an efficient randomized algorithm for finding approximate solutions to it. Moreover, we show that the expected cost of a solution found by the randomized algorithm differs from the optimal solution only by a constant factor. For the second approach we propose a simple method for sampling orders for 0–1 vectors that is based on the consecutive ones property. For analyzing orders, we discuss three different methods. First, we give an algorithm for clustering sets of orders. The algorithm is a variant of Lloyd's iteration for solving the k-means problem. We also give two different approaches for mapping orders to vectors in a high-dimensional Euclidean space. These mappings are used on one hand for clustering, and on the other hand for creating two dimensional visualizations (scatterplots) for sets of orders. Finally, we discuss randomization testing in case of orders. To this end we propose an MCMC algorithm for creating random sets of orders that preserve certain well defined properties of a given set of orders. The random data sets can be used to assess the statistical significance of the results obtained e.g. by clustering

Using and extending itemsets in data mining : query approximation, dense itemsets, and tiles

Frequent itemsets are one of the best known concepts in data mining, and there is active research in itemset mining algorithms. An itemset is frequent in a database if its items co-occur in sufficiently many records. This thesis addresses two questions related to frequent itemsets. The first question is raised by a method for approximating logical queries by an inclusion-exclusion sum truncated to the terms corresponding to the frequent itemsets: how good are the approximations thereby obtained? The answer is twofold: in theory, the worst-case bound for the algorithm is very large, and a construction is given that shows the bound to be tight; but in practice, the approximations tend to be much closer to the correct answer than in the worst case. While some other algorithms based on frequent itemsets yield even better approximations, they are not as widely applicable. The second question concerns extending the definition of frequent itemsets to relax the requirement of perfect co-occurrence: highly correlated items may form an interesting set, even if they never co-occur in a single record. The problem is to formalize this idea in a way that still admits efficient mining algorithms. Two different approaches are used. First, dense itemsets are defined in a manner similar to the usual frequent itemsets and can be found using a modification of the original itemset mining algorithm. Second, tiles are defined in a different way so as to form a model for the whole data, unlike frequent and dense itemsets. A heuristic algorithm based on spectral properties of the data is given and some of its properties are explored.Yksi tiedon louhinnan tunnetuimmista käsitteistä ovat kattavat joukot, ja niiden etsintäalgoritmeja tutkitaan aktiivisesti. Joukko on tietokannassa kattava, jos sen alkiot esiintyvät yhdessä riittävän monessa tietueessa. Väitöskirjassa käsitellään kahta kattaviin joukkoihin liittyvää kysymystä. Ensimmäinen liittyy algoritmiin, jolla arvioidaan loogisten kyselyjen tuloksia laskemalla inkluusio-ekskluusio-summa pelkästään kattavilla joukoilla; kysymys on, kuinka hyviä arvioita näin saadaan. Väitöskirjassa annetaan kaksi vastausta: Teoriassa algoritmin pahimman tapauksen raja on hyvin suuri, ja vastaesimerkillä osoitetaan, että raja on tiukka. Käytännössä arviot ovat paljon lähempänä oikeaa tulosta kuin teoreettinen raja antaa ymmärtää. Arvioita vertaillaan eräisiin muihin algoritmeihin, joiden tulokset ovat vielä parempia mutta jotka eivät ole yhtä yleisesti sovellettavissa. Toinen kysymys koskee kattavien joukkojen määritelmän yleistämistä siten, että täydellisen yhteisesiintymisen vaatimuksesta tingitään. Joukko korreloituneita alkioita voi olla kiinnostava, vaikka alkiot eivät koskaan esiintyisi kaikki samassa tietueessa. Ongelma on tämän ajatuksen muuttaminen sellaiseksi määritelmäksi, että tehokkaita louhinta-algoritmeja voidaan käyttää. Väitöskirjassa esitetään kaksi lähestymistapaa. Ensinnäkin tiheät kattavat joukot määritellään samanlaiseen tapaan kuin tavalliset kattavat joukot, ja ne voidaan löytää samantyyppisellä algoritmilla. Toiseksi määritellään laatat, jotka muodostavat koko datalle mallin, toisin kuin kattavat ja tiheät kattavat joukot. Laattojen etsimistä varten kuvataan datan spektraalisiin ominaisuuksiin perustuva heuristiikka, jonka eräitä ominaisuuksia tutkitaan.reviewe