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12
Finding Regional Colocation Patterns for Sets of Continuous Variables, under review
"... This paper proposes a novel framework for mining regional colocation patterns with respect to sets of continuous variables in spatial datasets. The goal is to identify regions in which multiple continuous variables with values from the wings of their statistical distribution are colocated. A coloc ..."
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Cited by 11 (9 self)
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This paper proposes a novel framework for mining regional colocation patterns with respect to sets of continuous variables in spatial datasets. The goal is to identify regions in which multiple continuous variables with values from the wings of their statistical distribution are colocated. A colocation mining framework is introduced that operates in the continuous domain without the need for discretization and which views regional colocation mining as a clustering problem in which an externally given fitness function has to be maximized. Interestingness of colocation patterns is assessed using products of zscores of the relevant continuous variables. The proposed framework is evaluated by a domain expert in a case study that analyzes chemical concentrations in Texas water wells centering on colocation patterns involving Arsenic. Our approach was able to identify known and unknown regional colocation patterns, and different sets of algorithm parameters lead to the characterization of arsenic distribution at different scales. Moreover, inconsistent colocation sets were found for regions in South Texas and West Texas that can be clearly attributed to geological differences in the two regions, emphasizing the need for regional colocation mining techniques. Moreover, a novel, prototypebased region discovery algorithm named CLEVER is introduced that uses randomized hill climbing, and searches a variable number of clusters and larger neighborhood sizes. Keywords spatial data mining, regional colocation mining, regional data mining, clustering, finding associations between continuous variables. 1.
An Association Analysis Approach to Biclustering
"... The discovery of biclusters, which denote groups of items that show coherent values across a subset of all the transactions in a data set, is an important type of analysis performed on realvalued data sets in various domains, such as biology. Several algorithms have been proposed to find different ..."
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Cited by 9 (5 self)
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The discovery of biclusters, which denote groups of items that show coherent values across a subset of all the transactions in a data set, is an important type of analysis performed on realvalued data sets in various domains, such as biology. Several algorithms have been proposed to find different types of biclusters in such data sets. However, these algorithms are unable to search the space of all possible biclusters exhaustively. Pattern mining algorithms in association analysis also essentially produce biclusters as their result, since the patterns consist of items that are supported by a subset of all the transactions. However, a major limitation of the numerous techniques developed in association analysis is that they are only able to analyze data sets with binary and/or categorical variables, and their application to realvalued data sets often involves some lossy transformation such as discretization or binarization of the attributes. In
Mining Bisets in Numerical Data
"... Abstract. Thanks to an important research effort the last few years, inductive queries on set patterns and complete solvers which can evaluate them on large 0/1 data sets have been proved extremely useful. However, for many application domains, the raw data is numerical (matrices of real numbers who ..."
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Cited by 2 (0 self)
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Abstract. Thanks to an important research effort the last few years, inductive queries on set patterns and complete solvers which can evaluate them on large 0/1 data sets have been proved extremely useful. However, for many application domains, the raw data is numerical (matrices of real numbers whose dimensions denote objects and properties). Therefore, using efficient 0/1 mining techniques needs for tedious Boolean property encoding phases. This is, e.g., the case, when considering microarray data mining and its impact for knowledge discovery in molecular biology. We consider the possibility to mine directly numerical data to extract collections of relevant bisets, i.e., couples of associated sets of objects and attributes which satisfy some userdefined constraints. Not only we propose a new pattern domain but also we introduce a complete solver for computing the socalled numerical bisets. Preliminary experimental validation is given. 1
Discovery of errortolerant biclusters from noisy gene expression data
 Bioinformatics
, 2011
"... An important analysis performed on microarray geneexpression data is to discover biclusters, which denote groups of genes that are coherently expressed for a subset of conditions. Various biclustering algorithms have been proposed to find different types of biclusters from these realvalued geneex ..."
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Cited by 2 (0 self)
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An important analysis performed on microarray geneexpression data is to discover biclusters, which denote groups of genes that are coherently expressed for a subset of conditions. Various biclustering algorithms have been proposed to find different types of biclusters from these realvalued geneexpression data sets. However, these algorithms suffer from several limitations such as inability to explicitly handle errors/noise in the data; difficulty in discovering small bicliusters due to their topdown approach; inability of some of the approaches to find overlapping biclusters, which is crucial as many genes participate in multiple biological processes. Association pattern mining also produce biclusters as their result and can naturally address some of these limitations. However, traditional association mining only finds exact biclusters, which
A novel errortolerant frequent itemset model for binary and realvalued data
, 2009
"... Frequent pattern mining has been successfully applied to a broad range of applications, however, it has two major drawbacks, which limits its applicability to several domains. First, as the traditional ‘exact ’ model of frequent pattern mining uses a strict definition of support, it limits the recov ..."
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Cited by 2 (2 self)
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Frequent pattern mining has been successfully applied to a broad range of applications, however, it has two major drawbacks, which limits its applicability to several domains. First, as the traditional ‘exact ’ model of frequent pattern mining uses a strict definition of support, it limits the recovery of frequent itemset patterns in reallife data sets where the patterns may be fragmented due to random noise/errors. Second, as traditional frequent pattern mining algorithms works with only binary or boolean attributes, it requires transformation of realvalued attributes to binary attributes, which often results in loss of information. As many of the reallife data sets are both noisy and realvalued in nature, past approaches have tried to independently address these issues and there is no systematic approach that addresses both of these issues together. In this paper, we propose a novel ErrorTolerant Frequent Itemset (ETFI) model for binary as well as realvalued data. We also propose a bottomup pattern mining algorithm to sequentially discover all ETFIs from both types of data sets. To illustrate the efficacy of our proposed ETFI approach, we use two realvalued S.Cerevisiae microarray geneexpression data sets and evaluate the patterns obtained in terms of their functional coherence as evaluated using the GObased functional enrichment analysis. Our results clearly demonstrate the importance of directly accounting for errors/noise in the data. Finally, the statistical significance of the discovered ETFIs as estimated by using two randomization tests, reveal that discovered ETFIs are indeed biologically meaningful and are neither obtained by random chance nor capture random structure in the data. The source codes as well as data sets used in this study are made available at the following website:
Abstract Approximating Representations for Large Numerical Databases
"... The paper introduces a notion of support for realvalued functions. It is shown how to approximate supports of a large class of functions based on supports of so called polynomial itemsets, which can efficiently be mined using an Aprioristyle algorithm. An upper bound for the error of such an approx ..."
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The paper introduces a notion of support for realvalued functions. It is shown how to approximate supports of a large class of functions based on supports of so called polynomial itemsets, which can efficiently be mined using an Aprioristyle algorithm. An upper bound for the error of such an approximation can be reliably computed. The concept of an approximating representation was introduced, which extends the idea of concise representations to numerical data. It has been shown that many standard statistical modelling tasks such as nonlinear regression and least squares curve fitting can efficiently be solved using only the approximating representation, without accessing the original data at all. Since many of those methods traditionally require several passes over the data, our approach makes it possible to use such methods with huge datasets and data streams where several repeated scans are very costly or outright impossible. 1 Introduction and
Approximating Representations for Large Numerical Databases
"... The paper introduces a notion of support for realvalued functions. It is shown how to approximate supports of a large class of functions based on supports of so called polynomial itemsets, which can efficiently be mined using an Aprioristyle algorithm. An upper bound for the error of such an approx ..."
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The paper introduces a notion of support for realvalued functions. It is shown how to approximate supports of a large class of functions based on supports of so called polynomial itemsets, which can efficiently be mined using an Aprioristyle algorithm. An upper bound for the error of such an approximation can be reliably computed. The concept of an approximating representation was introduced, which extends the idea of concise representations to numerical data. It has been shown that many standard statistical modelling tasks such as nonlinear regression and least squares curve fitting can efficiently be solved using only the approximating representation, without accessing the original data at all. Since many of those methods traditionally require several passes over the data, our approach makes it possible to use such methods with huge datasets and data streams where several repeated scans are very costly or outright impossible. 1 Introduction and
2012 IEEE 12th International Conference on Data Mining Workshops Supporting the Discovery of Relevant Topological Patterns in Attributed Graphs
"... Abstract—We propose TopGraphVisualizer, a tool to support the discovery of relevant topological patterns in attributed graphs. It relies on a new pattern detection method that crucially needs for sophisticated postprocessing and visualization. A topological pattern is defined as a set of vertex attr ..."
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Abstract—We propose TopGraphVisualizer, a tool to support the discovery of relevant topological patterns in attributed graphs. It relies on a new pattern detection method that crucially needs for sophisticated postprocessing and visualization. A topological pattern is defined as a set of vertex attributes and topological properties (i.e., properties that characterize the role of a vertex within a graph) that strongly covary over the vertices of the graph. For instance, such a pattern in a coauthorship attributed graph where vertices represent authors, edges encode coauthorship, and vertex attributes reveal the number of publications in several journals, could be “the higher the number of publications in IEEE ICDM, the higher the closeness centrality of the vertex within the graph”. Two different ways of navigation through the topological patterns and the related graph data are provided to the enduser. We exploit graph visualization and exploration techniques from the open platform Gephi. As an illustrative scenario, we consider a coautorship attributed graph built from DBLP digital library and a video has been produced that describe the main possibilities of the TopGraphVisualizer software. KeywordsTopological patterns, attributed graphs, structural correlation. I.
Article MultiCore Parallel Gradual Pattern Mining Based on MultiPrecision Fuzzy Orderings
, 2013
"... algorithms ..."