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

Predictability, complexity and learning

We define {\em predictive information} $I_{\rm pred} (T)$ as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times $T$: $I_{\rm pred} (T)$ can remain finite, grow logarithmically, or grow as a fractional power law. If the time series allows us to learn a model with a finite number of parameters, then $I_{\rm pred} (T)$ grows logarithmically with a coefficient that counts the dimensionality of the model space. In contrast, power--law growth is associated, for example, with the learning of infinite parameter (or nonparametric) models such as continuous functions with smoothness constraints. There are connections between the predictive information and measures of complexity that have been defined both in learning theory and in the analysis of physical systems through statistical mechanics and dynamical systems theory. Further, in the same way that entropy provides the unique measure of available information consistent with some simple and plausible conditions, we argue that the divergent part of $I_{\rm pred} (T)$ provides the unique measure for the complexity of dynamics underlying a time series. Finally, we discuss how these ideas may be useful in different problems in physics, statistics, and biology.Comment: 53 pages, 3 figures, 98 references, LaTeX2

On Interpretable Approaches to Cluster, Classify and Represent Multi-Subspace Data via Minimum Lossy Coding Length based on Rate-Distortion Theory

To cluster, classify and represent are three fundamental objectives of learning from high-dimensional data with intrinsic structure. To this end, this paper introduces three interpretable approaches, i.e., segmentation (clustering) via the Minimum Lossy Coding Length criterion, classification via the Minimum Incremental Coding Length criterion and representation via the Maximal Coding Rate Reduction criterion. These are derived based on the lossy data coding and compression framework from the principle of rate distortion in information theory. These algorithms are particularly suitable for dealing with finite-sample data (allowed to be sparse or almost degenerate) of mixed Gaussian distributions or subspaces. The theoretical value and attractive features of these methods are summarized by comparison with other learning methods or evaluation criteria. This summary note aims to provide a theoretical guide to researchers (also engineers) interested in understanding 'white-box' machine (deep) learning methods

Object-based video representations: shape compression and object segmentation

Object-based video representations are considered to be useful for easing the process of multimedia content production and enhancing user interactivity in multimedia productions. Object-based video presents several new technical challenges, however. Firstly, as with conventional video representations, compression of the video data is a requirement. For object-based representations, it is necessary to compress the shape of each video object as it moves in time. This amounts to the compression of moving binary images. This is achieved by the use of a technique called context-based arithmetic encoding. The technique is utilised by applying it to rectangular pixel blocks and as such it is consistent with the standard tools of video compression. The blockbased application also facilitates well the exploitation of temporal redundancy in the sequence of binary shapes. For the first time, context-based arithmetic encoding is used in conjunction with motion compensation to provide inter-frame compression. The method, described in this thesis, has been thoroughly tested throughout the MPEG-4 core experiment process and due to favourable results, it has been adopted as part of the MPEG-4 video standard. The second challenge lies in the acquisition of the video objects. Under normal conditions, a video sequence is captured as a sequence of frames and there is no inherent information about what objects are in the sequence, not to mention information relating to the shape of each object. Some means for segmenting semantic objects from general video sequences is required. For this purpose, several image analysis tools may be of help and in particular, it is believed that video object tracking algorithms will be important. A new tracking algorithm is developed based on piecewise polynomial motion representations and statistical estimation tools, e.g. the expectationmaximisation method and the minimum description length principle

An information-theoretic framework for semantic-multimedia retrieval

This article is set in the context of searching text and image repositories by keyword. We develop a unified probabilistic framework for text, image, and combined text and image retrieval that is based on the detection of keywords (concepts) using automated image annotation technology. Our framework is deeply rooted in information theory and lends itself to use with other media types. We estimate a statistical model in a multimodal feature space for each possible query keyword. The key element of our framework is to identify feature space transformations that make them comparable in complexity and density. We select the optimal multimodal feature space with a minimum description length criterion from a set of candidate feature spaces that are computed with the average-mutual-information criterion for the text part and hierarchical expectation maximization for the visual part of the data. We evaluate our approach in three retrieval experiments (only text retrieval, only image retrieval, and text combined with image retrieval), verify the framework’s low computational complexity, and compare with existing state-of-the-art ad-hoc models