The Minimum Description Length Principle for Pattern Mining: A Survey

This is about the Minimum Description Length (MDL) principle applied to pattern mining. The length of this description is kept to the minimum. Mining patterns is a core task in data analysis and, beyond issues of efficient enumeration, the selection of patterns constitutes a major challenge. The MDL principle, a model selection method grounded in information theory, has been applied to pattern mining with the aim to obtain compact high-quality sets of patterns. After giving an outline of relevant concepts from information theory and coding, as well as of work on the theory behind the MDL and similar principles, we review MDL-based methods for mining various types of data and patterns. Finally, we open a discussion on some issues regarding these methods, and highlight currently active related data analysis problems

{MDL4BMF}: Minimum Description Length for Boolean Matrix Factorization

Matrix factorizations—where a given data matrix is approximated by a prod- uct of two or more factor matrices—are powerful data mining tools. Among other tasks, matrix factorizations are often used to separate global structure from noise. This, however, requires solving the ‘model order selection problem’ of determining where fine-grained structure stops, and noise starts, i.e., what is the proper size of the factor matrices. Boolean matrix factorization (BMF)—where data, factors, and matrix product are Boolean—has received increased attention from the data mining community in recent years. The technique has desirable properties, such as high interpretability and natural sparsity. However, so far no method for selecting the correct model order for BMF has been available. In this paper we propose to use the Minimum Description Length (MDL) principle for this task. Besides solving the problem, this well-founded approach has numerous benefits, e.g., it is automatic, does not require a likelihood function, is fast, and, as experiments show, is highly accurate. We formulate the description length function for BMF in general—making it applicable for any BMF algorithm. We discuss how to construct an appropriate encoding, starting from a simple and intuitive approach, we arrive at a highly efficient data-to-model based encoding for BMF. We extend an existing algorithm for BMF to use MDL to identify the best Boolean matrix factorization, analyze the complexity of the problem, and perform an extensive experimental evaluation to study its behavior

Filling in the blanks - Krimp minimisation for missing data

Many data sets are incomplete. For correct analysis of such data, one can either use algorithms that are designed to handle missing data or use imputation. Imputation has the benefit that it allows for any type of data analysis. Obviously, this can only lead to proper conclusions if the provided data completion is both highly accurate and maintains all statistics of the original data. In this paper, we present three data completion methods that are built on the MDL-based KRIMP algorithm. Here, we also follow the MDL principle, i.e. the completed database that can be compressed best, is the best completion because it adheres best to the patterns in the data. By using local patterns, as opposed to a global model, KRIMP captures the structure of the data in detail. Experiments show that both in terms of accuracy and expected differences of any marginal, better data reconstructions are provided than the state of the art, Structural EM.