Revisiting Numerical Pattern Mining with Formal Concept Analysis

In this paper, we investigate the problem of mining numerical data in the framework of Formal Concept Analysis. The usual way is to use a scaling procedure --transforming numerical attributes into binary ones-- leading either to a loss of information or of efficiency, in particular w.r.t. the volume of extracted patterns. By contrast, we propose to directly work on numerical data in a more precise and efficient way, and we prove it. For that, the notions of closed patterns, generators and equivalent classes are revisited in the numerical context. Moreover, two original algorithms are proposed and used in an evaluation involving real-world data, showing the predominance of the present approach

Empirical analysis of rough set categorical clustering techniques based on rough purity and value set

Clustering a set of objects into homogeneous groups is a fundamental operation in data mining. Recently, attention has been put on categorical data clustering, where data objects are made up of non-numerical attributes. The implementation of several existing categorical clustering techniques is challenging as some are unable to handle uncertainty and others have stability issues. In the process of dealing with categorical data and handling uncertainty, the rough set theory has become well-established mechanism in a wide variety of applications including databases. The recent techniques such as Information-Theoretic Dependency Roughness (ITDR), Maximum Dependency Attribute (MDA) and Maximum Significance Attribute (MSA) outperformed their predecessor approaches like Bi-Clustering (BC), Total Roughness (TR), Min-Min Roughness (MMR), and standard-deviation roughness (SDR). This work explores the limitations and issues of ITDR, MDA and MSA techniques on data sets where these techniques fails to select or faces difficulty in selecting their best clustering attribute. Accordingly, two alternative techniques named Rough Purity Approach (RPA) and Maximum Value Attribute (MVA) are proposed. The novelty of both proposed approaches is that, the RPA presents a new uncertainty definition based on purity of rough relational data base whereas, the MVA unlike other rough set theory techniques uses the domain knowledge such as value set combined with number of clusters (NoC). To show the significance, mathematical and theoretical basis for proposed approaches, several propositions are illustrated. Moreover, the recent rough categorical techniques like MDA, MSA, ITDR and classical clustering technique like simple K-mean are used for comparison and the results are presented in tabular and graphical forms. For experiments, data sets from previously utilized research cases, a real supply base management (SBM) data set and UCI repository are utilized. The results reveal significant improvement by proposed techniques for categorical clustering in terms of purity (21%), entropy (9%), accuracy (16%), rough accuracy (11%), iterations (99%) and time (93%). vi

Compressive Mining: Fast and Optimal Data Mining in the Compressed Domain

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance estimation when the data are represented using different sets of coefficients is still a largely unexplored area. This work studies the optimization problems related to obtaining the \emph{tightest} lower/upper bound on Euclidean distances when each data object is potentially compressed using a different set of orthonormal coefficients. Our technique leads to tighter distance estimates, which translates into more accurate search, learning and mining operations \textit{directly} in the compressed domain. We formulate the problem of estimating lower/upper distance bounds as an optimization problem. We establish the properties of optimal solutions, and leverage the theoretical analysis to develop a fast algorithm to obtain an \emph{exact} solution to the problem. The suggested solution provides the tightest estimation of the $L_2$-norm or the correlation. We show that typical data-analysis operations, such as k-NN search or k-Means clustering, can operate more accurately using the proposed compression and distance reconstruction technique. We compare it with many other prevalent compression and reconstruction techniques, including random projections and PCA-based techniques. We highlight a surprising result, namely that when the data are highly sparse in some basis, our technique may even outperform PCA-based compression. The contributions of this work are generic as our methodology is applicable to any sequential or high-dimensional data as well as to any orthogonal data transformation used for the underlying data compression scheme.Comment: 25 pages, 20 figures, accepted in VLD

Mining Biclusters of Similar Values with Triadic Concept Analysis

Biclustering numerical data became a popular data-mining task in the beginning of 2000's, especially for analysing gene expression data. A bicluster reflects a strong association between a subset of objects and a subset of attributes in a numerical object/attribute data-table. So called biclusters of similar values can be thought as maximal sub-tables with close values. Only few methods address a complete, correct and non redundant enumeration of such patterns, which is a well-known intractable problem, while no formal framework exists. In this paper, we introduce important links between biclustering and formal concept analysis. More specifically, we originally show that Triadic Concept Analysis (TCA), provides a nice mathematical framework for biclustering. Interestingly, existing algorithms of TCA, that usually apply on binary data, can be used (directly or with slight modifications) after a preprocessing step for extracting maximal biclusters of similar values.Comment: Concept Lattices and their Applications (CLA) (2011

Differential Privacy in Metric Spaces: Numerical, Categorical and Functional Data Under the One Roof

We study Differential Privacy in the abstract setting of Probability on metric spaces. Numerical, categorical and functional data can be handled in a uniform manner in this setting. We demonstrate how mechanisms based on data sanitisation and those that rely on adding noise to query responses fit within this framework. We prove that once the sanitisation is differentially private, then so is the query response for any query. We show how to construct sanitisations for high-dimensional databases using simple 1-dimensional mechanisms. We also provide lower bounds on the expected error for differentially private sanitisations in the general metric space setting. Finally, we consider the question of sufficient sets for differential privacy and show that for relaxed differential privacy, any algebra generating the Borel $\sigma$-algebra is a sufficient set for relaxed differential privacy.Comment: 18 Page

Mining the Web for Lexical Knowledge to Improve Keyphrase Extraction: Learning from Labeled and Unlabeled Data.

A journal article is often accompanied by a list of keyphrases, composed of about five to fifteen important words and phrases that capture the article’s main topics. Keyphrases are useful for a variety of purposes, including summarizing, indexing, labeling, categorizing, clustering, highlighting, browsing, and searching. The task of automatic keyphrase extraction is to select keyphrases from within the text of a given document. Automatic keyphrase extraction makes it feasible to generate keyphrases for the huge number of documents that do not have manually assigned keyphrases. Good performance on this task has been obtained by approaching it as a supervised learning problem. An input document is treated as a set of candidate phrases that must be classified as either keyphrases or non-keyphrases. To classify a candidate phrase as a keyphrase, the most important features (attributes) appear to be the frequency and location of the candidate phrase in the document. Recent work has demonstrated that it is also useful to know the frequency of the candidate phrase as a manually assigned keyphrase for other documents in the same domain as the given document (e.g., the domain of computer science). Unfortunately, this keyphrase-frequency feature is domain-specific (the learning process must be repeated for each new domain) and training-intensive (good performance requires a relatively large number of training documents in the given domain, with manually assigned keyphrases). The aim of the work described here is to remove these limitations. In this paper, I introduce new features that are conceptually related to keyphrase-frequency and I present experiments that show that the new features result in improved keyphrase extraction, although they are neither domain-specific nor training-intensive. The new features are generated by issuing queries to a Web search engine, based on the candidate phrases in the input document. The feature values are calculated from the number of hits for the queries (the number of matching Web pages). In essence, these new features are derived by mining lexical knowledge from a very large collection of unlabeled data, consisting of approximately 350 million Web pages without manually assigned keyphrases

A fractal fragmentation model for rockfalls

The final publication is available at Springer via http://dx.doi.org/10.1007/s10346-016-0773-8The impact-induced rock mass fragmentation in a rockfall is analyzed by comparing the in situ block size distribution (IBSD) of the rock mass detached from the cliff face and the resultant rockfall block size distribution (RBSD) of the rockfall fragments on the slope. The analysis of several inventoried rockfall events suggests that the volumes of the rockfall fragments can be characterized by a power law distribution. We propose the application of a three-parameter rockfall fractal fragmentation model (RFFM) for the transformation of the IBSD into the RBSD. A discrete fracture network model is used to simulate the discontinuity pattern of the detached rock mass and to generate the IBSD. Each block of the IBSD of the detached rock mass is an initiator. A survival rate is included to express the proportion of the unbroken blocks after the impact on the ground surface. The model was calibrated using the volume distribution of a rockfall event in Vilanova de Banat in the Cadí Sierra, Eastern Pyrenees, Spain. The RBSD was obtained directly in the field, by measuring the rock block fragments deposited on the slope. The IBSD and the RBSD were fitted by exponential and power law functions, respectively. The results show that the proposed fractal model can successfully generate the RBSD from the IBSD and indicate the model parameter values for the case study.Peer ReviewedPostprint (author's final draft