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.
The missing values can be simply ignored in methods that rely in itemization to mine the biclusters. Henriques & Madeira @cite_30 also proposed the use of additional items, specially handled according to a level of relaxation imposed by the user.
@cite_30
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Missing values widely exist in many real-world datasets, which hinders the performing of advanced data analytics. Properly filling these missing values is crucial but challenging, especially when the missing rate is high. Many approaches have been proposed for missing value imputation (MVI), but they are mostly heuristics-based, lacking a principled foundation and do not perform satisfactorily in practice. In this paper, we propose a probabilistic framework based on deep generative models for MVI. Under this framework, imputing the missing entries amounts to seeking a fixed-point solution between two conditional distributions defined on the missing entries and latent variables respectively. These distributions are parameterized by deep neural networks (DNNs) which possess high approximation power and can capture the nonlinear relationships between missing entries and the observed values. The learning of weight parameters of DNNs is performed by maximizing an approximation of the log-likelihood of observed values. We conducted extensive evaluation on 13 datasets and compared with 11 baselines methods, where our methods largely outperforms the baselines. 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. This paper proposes to utilize information within incomplete instances (instances with missing values) when estimating missing values. Accordingly, a simple and efficient nonparametric iterative imputation algorithm, called the NIIA method, is designed for iteratively imputing missing target values. The NIIA method imputes each missing value several times until the algorithm converges. In the first iteration, all the complete instances are used to estimate missing values. The information within incomplete instances is utilized since the second imputation iteration. We conduct some experiments for evaluating the efficiency, and demonstrate: (1) the utilization of information within incomplete instances is of benefit to easily capture the distribution of a dataset; and (2) the NIIA method outperforms the existing methods in accuracy, and this advantage is clearly highlighted when datasets have a high missing ratio. Recommender problems with large and dynamic item pools are ubiquitous in web applications like content optimization, online advertising and web search. Despite the availability of rich item meta-data, excess heterogeneity at the item level often requires inclusion of item-specific "factors" (or weights) in the model. However, since estimating item factors is computationally intensive, it poses a challenge for time-sensitive recommender problems where it is important to rapidly learn factors for new items (e.g., news articles, event updates, tweets) in an online fashion. In this paper, we propose a novel method called FOBFM (Fast Online Bilinear Factor Model) to learn item-specific factors quickly through online regression. The online regression for each item can be performed independently and hence the procedure is fast, scalable and easily parallelizable. However, the convergence of these independent regressions can be slow due to high dimensionality. The central idea of our approach is to use a large amount of historical data to initialize the online models based on offline features and learn linear projections that can effectively reduce the dimensionality. We estimate the rank of our linear projections by taking recourse to online model selection based on optimizing predictive likelihood. Through extensive experiments, we show that our method significantly and uniformly outperforms other competitive methods and obtains relative lifts that are in the range of 10-15 in terms of predictive log-likelihood, 200-300 for a rank correlation metric on a proprietary My Yahoo! dataset; it obtains 9 reduction in root mean squared error over the previously best method on a benchmark MovieLens dataset using a time-based train test data split.