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.
In fact, after imposing discretization, we have better proposals than @cite_12 , especially when we consider the connection between biclustering, FPM and FCA. Notice that we can extract CVC biclusters from quantitative-itemsets (and vice-versa), and (quantitative) association rules are mined from (quantitative-)frequent itemsets. Veroneze @cite_1 also showed that well-known heuristic-based biclustering algorithms can have a poor performance when trying to identify the existing biclusters in a simple and controlled scenario, thus fully favouring the use of efficient enumerative algorithms, such as the ones provided in FPM and FCA literature and the RIn-Close family @cite_1 .
@cite_1 @cite_12
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Biclustering has proved to be a powerful data analysis technique due to its wide success in various application domains. However, the existing literature presents efficient solutions only for enumerating maximal biclusters with constant values, or heuristic-based approaches which can not find all biclusters or even support the maximality of the obtained biclusters. Here, we present a general family of biclustering algorithms for enumerating all maximal biclusters with (i) constant values on rows, (ii) constant values on columns, or (iii) coherent values. Versions for perfect and for perturbed biclusters are provided. Our algorithms have four key properties (just the algorithm for perturbed biclusters with coherent values fails to exhibit the first property): they are (1) efficient (take polynomial time per pattern), (2) complete (find all maximal biclusters), (3) correct (all biclusters attend the user-defined measure of similarity), and (4) non-redundant (all the obtained biclusters are maximal and the same bicluster is not enumerated twice). They are based on a generalization of an efficient formal concept analysis algorithm called In-Close2. Experimental results point to the necessity of having efficient enumerative biclustering algorithms and provide a valuable insight into the scalability of our family of algorithms and its sensitivity to user-defined parameters. We define the problem of biclustering on heterogeneous data, that is, data of various types (binary, numeric, etc.). This problem has not yet been investigated in the biclustering literature.We propose a new method, HBC (Heterogeneous BiClustering), designed to extract biclus- ters from heterogeneous, large-scale, sparse data matrices. The goal of this method is to handle medical data gathered by hospitals (on patients, stays, acts, diagnoses, prescriptions, etc.) and to provide valuable insight on such data. HBC takes advantage of the data sparsity and uses a con- structive greedy heuristic to build a large number of possibly overlapping biclusters. The proposed method is successfully compared with a stan- dard biclustering algorithm on small-size numeric data. Experiments on real-life data sets further assert its scalability and efficiency.