This paper presents a novel enumerative biclustering algorithm to directly mine all maximal biclusters in mixed-attribute datasets (containing both numerical and categorical attributes), with or without missing values. The proposal is an extension of RIn-Close_CVC, which was originally conceived to mine perfect or perturbed biclusters with constant values on columns solely from numerical datasets, and without missing values. Even endowed with additional and more general features, the extended RIn-Close_CVC retains four key properties: (1) efficiency, (2) completeness, (3) correctness, and (4) non-redundancy. Our proposal is the first one to deal with mixed-attribute datasets without requiring any pre-processing step, such as discretization and itemization of real-valued attributes. This is a decisive aspect, because discretization and itemization implies a priori decisions, with information loss and no clear control over the consequences. On the other hand, even having to specify a priori an individual threshold for each numerical attribute, that will be used to indicate internal consistency per attribute, each threshold will be applied during the construction of the biclusters, shaping the peculiarities of the data distribution. We also explore the strong connection between biclustering and frequent pattern mining to (1) provide filters to select a compact bicluster set that exhibits high relevance and low redundancy, and (2) in the case of labeled datasets, automatically present the biclusters in a user-friendly and intuitive form, by means of quantitative class association rules. Our experimental results showed that the biclusters yield a parsimonious set of relevant rules, providing useful and interpretable models for five mixed-attribute labeled datasets.
BicPAM @cite_30 and BiC2PAM @cite_18 also relies on discretization, itemization, and the usage of a traditional FPM algorithm to mine the biclusters. BiC2PAM extends BicPAM to incorporate constraints derived from background knowledge in the mining process. BicPAM and BiC2PAM are available in a free bicluster software called BicPAMS @cite_11 .
@cite_30 @cite_18 @cite_11
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Mining matrices to find relevant biclusters, subsets of rows exhibiting a coherent pattern over a subset of columns, is a critical task for a wide-set of biomedical and social applications. Since biclustering is a challenging combinatorial optimization task, existing approaches place restrictions on the allowed structure, coherence and quality of biclusters. Biclustering approaches relying on pattern mining (PM) allow an exhaustive yet efficient space exploration together with the possibility to discover flexible structures of biclusters with parameterizable coherency and noise-tolerance. Still, state-of-the-art contributions are dispersed and the potential of their integration remains unclear.This work proposes a structured and integrated view of the contributions of state-of-the-art PM-based biclustering approaches, makes available a set of principles for a guided definition of new PM-based biclustering approaches, and discusses their relevance for applications in pattern recognition. Empirical evidence shows that these principles guarantee the robustness, efficiency and flexibility of PM-based biclustering. HighlightsPattern mining (PM) searches enable flexible, exhaustive and efficient biclusteringIntegration of existing dispersed PM-inspired contributions for biclustering.Principles for guided design and evaluation of new PM-based biclustering approachesPM-based biclustering solutions have parameterizable coherency and quality. The application of frequent patterns in classification has demonstrated its power in recent studies. It often adopts a two-step approach: frequent pattern (or classification rule) mining followed by feature selection (or rule ranking). However, this two-step process could be computationally expensive, especially when the problem scale is large or the minimum support is low. It was observed that frequent pattern mining usually produces a huge number of "patterns" that could not only slow down the mining process but also make feature selection hard to complete. In this paper, we propose a direct discriminative pattern mining approach, DDPMine, to tackle the efficiency issue arising from the two-step approach. DDPMine performs a branch-and-bound search for directly mining discriminative patterns without generating the complete pattern set. Instead of selecting best patterns in a batch, we introduce a "feature-centered" mining approach that generates discriminative patterns sequentially on a progressively shrinking FP-tree by incrementally eliminating training instances. The instance elimination effectively reduces the problem size iteratively and expedites the mining process. Empirical results show that DDPMine achieves orders of magnitude speedup without any downgrade of classification accuracy. It outperforms the state-of-the-art associative classification methods in terms of both accuracy and efficiency. In this paper, two supervised methods for enhancing the classification accuracy of the Nonnegative Matrix Factorization (NMF) algorithm are presented. The idea is to extend the NMF algorithm in order to extract features that enforce not only the spatial locality, but also the separability between classes in a discriminant manner. The first method employs discriminant analysis in the features derived from NMF. In this way, a two-phase discriminant feature extraction procedure is implemented, namely NMF plus Linear Discriminant Analysis (LDA). The second method incorporates the discriminant constraints inside the NMF decomposition. Thus, a decomposition of a face to its discriminant parts is obtained and new update rules for both the weights and the basis images are derived. The introduced methods have been applied to the problem of frontal face verification using the well-known XM2VTS database. Both methods greatly enhance the performance of NMF for frontal face verification Sequential pattern mining (SPM) is an important data mining problem with broad applications. SPM is a hard problem due to the huge number of intermediate subsequences to be considered. State of the art approaches for SPM (e.g., PrefixSpan 2001) are largely based on the pattern-growth approach, where for each frequent prefix subsequence, only its related suffix subsequences need to be considered, and the database is recursively projected into smaller ones. Many authors have promoted the use of constraints to focus on the most promising patterns according to the interests of the end user. The top-k SPM problem is also used to cope with the difficulty of thresholding and to control the number of solutions. State of the art methods developed for SPM and top-k SPM, though efficient, are locked into a rather rigid search strategy, and suffer from the lack of declarativity and flexibility. Indeed, adding new constraints usually amounts to changing the data-structures used in the core of the algorithm, and combining these new constraints often require new developments. Recent works (e.g. 2014; Negrevergne and Guns 2015) have investigated the use of Constraint Programming (CP) for SPM. However, despite their nice declarative aspects, all these modelings have scaling problems, due to the huge size of their constraint networks. To address this issue, we propose the Prefix-Projection global constraint, which encapsulates both the subsequence relation as well as the frequency constraint. Its filtering algorithm relies on the principle of projected databases which allows to keep in the variables domain, only values leading to a frequent pattern in the database. Prefix-Projection filtering algorithm enforces domain consistency on the variable succeeding the current frequent prefix in polynomial time. This global constraint also allows for a straightforward implementation of additional constraints such as size, item membership, regular expressions and any combination of them. Experimental results show that our approach clearly outperforms existing CP approaches and competes well with the state-of-the-art methods on large datasets for mining frequent sequential patterns, sequential patterns under various constraints, and top-k sequential patterns. Unlike existing CP methods, our approach achieves a better scalability.