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 @cite_12 , the authors presented a biclustering method designed to handle mixed-attribute datasets. This method uses a pre-processing step to simplify the data by means of discretization, and a constructive greedy heuristic to build the biclusters by iteratively adding columns. Their goal was, as expected, to detect CVC biclusters. To the best of Vandromme 's knowledge, this was the first method to handle mixed-attribute datasets in the biclustering literature @cite_12 .
@cite_12
2563966252 2145799156 1894726941 2100038249
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. We consider the problem of identifying a sparse set of relevant columns and rows in a large data matrix with highly corrupted entries. This problem of identifying groups from a collection of bipartite variables such as proteins and drugs, biological species and gene sequences, malware and signatures, etc is commonly referred to as biclustering or co-clustering. Despite its great practical relevance, and although several ad-hoc methods are available for biclustering, theoretical analysis of the problem is largely non-existent. The problem we consider is also closely related to structured multiple hypothesis testing, an area of statistics that has recently witnessed a flurry of activity. We make the following contributions 1. We prove lower bounds on the minimum signal strength needed for successful recovery of a bicluster as a function of the noise variance, size of the matrix and bicluster of interest. 2. We show that a combinatorial procedure based on the scan statistic achieves this optimal limit. 3. We characterize the SNR required by several computationally tractable procedures for biclustering including element-wise thresholding, column row average thresholding and a convex relaxation approach to sparse singular vector decomposition. 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. 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 real-valued 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 real-valued data sets often involves some lossy transformation such as discretization or binarization of the attributes. In this paper, we propose a novel association analysis framework for exhaustively and efficiently mining "range support" patterns from such a data set. On one hand, this framework reduces the loss of information incurred by the binarization- and discretization-based approaches, and on the other, it enables the exhaustive discovery of coherent biclusters. We compared the performance of our framework with two standard biclustering algorithms through the evaluation of the similarity of the cellular functions of the genes constituting the patterns biclusters derived by these algorithms from microarray data. These experiments show that the real-valued patterns discovered by our framework are better enriched by small biologically interesting functional classes. Also, through specific examples, we demonstrate the ability of the RAP framework to discover functionally enriched patterns that are not found by the commonly used biclustering algorithm ISA. The source code and data sets used in this paper, as well as the supplementary material, are available at http: www.cs.umn.edu vk gaurav rap.