Rank data, in which each row is a complete or partial ranking of available items (columns), is ubiquitous. It has been used to represent, for instance, preferences of users, the levels of gene expression, and the outcomes of sports events. While rank data has been analysed in data mining, pattern mining in such data has so far not received much attention. To alleviate this state of affairs, we introduce a novel pattern set mining approach. It is based on a semiring matrix factorisation framework. Rather than using the traditional linear algebra for matrix factorisation we employ the max-product semiring. Our semiring matrix factorisation framework is then applied to two tasks: sparse rank matrix factorisation and ranked tiling. Algorithms for these tasks are proposed, and their effectiveness is demonstrated on extensive experiments using both synthetic and real data.

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Subtyping cancer is key to an improved and more personalized prognosis/treatment. The increasing availability of tumor related molecular data provides the opportunity to identify molecular subtypes in a data-driven way. Molecular subtypes are defined as groups of samples that have a similar molecular mechanism at the origin of the carcinogenesis. The molecular mechanisms are reflected by subtype-specific mutational and expression features.

Data-driven subtyping is a complex problem as subtyping and identifying the molecular mechanisms that drive carcinogenesis are confounded problems. Many current integrative subtyping methods use global mutational and/or expression tumor profiles to group tumor samples in subtypes but do not explicitly extract the subtype-specific features. We therefore present a method that solves both tasks of subtyping and identification of subtype-specific features simultaneously. Hereto our method integrates mutational and expression data while taking into account the clonal properties of carcinogenesis. Key to our method is a formalisation of the problem as a \emph{rank matrix factorisation} of \emph{ranked data} that approaches the subtyping problem as \emph{multi-view bi-clustering}.

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We introduce the problem of \emph{rank matrix factorisation} (RMF). That is, we consider the decomposition of a rank matrix, in which each row is a (partial or complete) ranking of all columns. Rank matrices naturally appear in many applications of interest, such as sports competitions. Summarising such a rank matrix by two smaller matrices, in which one contains partial rankings that can be interpreted as local patterns, is therefore an important problem.

After introducing the general problem, we consider a specific instance called Sparse RMF, in which we enforce the rank profiles to be sparse, i.e., to contain many zeroes. We propose a greedy algorithm for this problem based on integer linear programming. Experiments on both synthetic and real data demonstrate the potential of rank matrix factorisation.

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Tiling is a well-known pattern mining technique. Traditionally, it discovers large areas of ones in binary databases or matrices, where an area is defined by a set of rows and a set of columns. %However, it cannot be applied on data that is not binary. In this paper, we introduce the novel problem of {\em ranked} tiling, which is concerned with finding interesting areas in ranked data. In this data, each transaction defines a complete ranking of the columns. Ranked data occurs naturally in applications like sports or other competitions. It is also a useful abstraction when dealing with numeric data in which the rows are incomparable.% due do incompatible scales.

We introduce a scoring function for ranked tiling, as well as an algorithm using constraint programming and optimization principles. We empirically evaluate the approach on both synthetic and real-life datasets, and demonstrate the applicability of the framework in several case studies. One case study involves a heterogeneous dataset concerning the discovery of biomarkers for different subtypes of breast cancer patients. An analysis of the tiles by a domain expert shows that our approach can lead to the discovery of novel insights.

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Most traditional biclustering algorithms identify biclusters with no or little overlap. In this paper, we introduce the problem of identifying staircases of biclusters. Such staircases may be indicative for causal relationships between columns and can not easily be identified by existing biclustering algorithms. Our formalization relies on a scoring function based on the Minimum Description Length principle. Furthermore, we propose a first algorithm for identifying staircase biclusters, based on a combination of local search and constraint programming. Experiments show that the approach is promising.

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This paper presents a novel approach to deriving probabilistic models that predict enrollment given applicant background and the amount of financial aid offered. Our Bayesian network models can be used to optimize various enrollment objectives. We present a novel efficient optimization algorithm that uses the models to maximize expected tuition revenue under capacity constraints including student-faculty ratio and accommodation. We demonstrate and evaluate our approach using four years of graduate admissions data from the Asian Institute of Technology, consisting of 7,788 applicants from 84 different countries. This data set is particularly challenging since reliable family income data is not available for students from most of these countries. Evaluating the Bayesian network model with 10-fold cross validation yields an ROC Az value of 0.8451, with a predictive accuracy of 82.70% at a threshold of 0.5. Comparing the results of the tuition revenue optimization model to the institute's current financial aid allocation practice shows that if single-term tuition revenue is the sole optimization criterion, the institute can achieve its current enrollment numbers while realizing significant savings in its financial aid budget. The prediction and optimization software is currently being incorporated into the institute's online admissions processing system.

@INPROCEEDINGS{levan2007, author={L. V. Thanh and P. Haddawy}, booktitle={2007 37th Annual Frontiers In Education Conference - Global Engineering: Knowledge Without Borders, Opportunities Without Passports}, title={Deriving financial aid optimization models from admissions data}, year={2007}, pages={F2A-7-F2A-12}, doi={10.1109/FIE.2007.4417959}, ISSN={0190-5848}, month={Oct}}