Matrix factorizations—where a given data matrix is approximated by a product 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 the proper rank of the factorization, that is, to answer where fine-grained structure stops, and where noise starts.Boolean Matrix Factorization (BMF)—where data, factors, and matrix product are Boolean—has in recent years received increased attention from the data mining community. The technique has desirable properties, such as high interpretability and natural sparsity. Yet, so far no method for selecting the correct model order for BMF has been available. In this article, we propose the use of the Minimum Description Length (MDL) principle for this task. Besides solving the problem, this well-founded approach has numerous benefits; for example, 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.

https://eda.mmci.uni-saarland.de/pubs/2012/mdl4bmf-miettinen,vreeken-techrep.pdf

MDL4BMF: Minimum Description Length for Boolean Matrix Factorization

The common graph Laplacian regularizer is well-established in semi-supervised learning and spectral dimensionality reduction. However, as a first-order regularizer, it can lead to degenerate functions in high-dimensional manifolds. The iterated graph Laplacian enables high-order regularization, but it has a high computational complexity and so cannot be applied to large problems. We introduce a new regularizer which is globally high order and so does not suffer from the degeneracy of the graph Laplacian regularizer, but is also sparse for efficient computation in semi-supervised learning applications. We reduce computational complexity by building a local first-order approximation of the manifold as a surrogate geometry, and construct our high-order regularizer based on local derivative evaluations therein. Experiments on human body shape and pose analysis demonstrate the effectiveness and efficiency of our method.

/pdf/local-high-order-regularization-on-data-manifolds-49x59vxu2z.pdf

Local high-order regularization on data manifolds

Using hand gestures as input in human–computer interaction is of everincreasing interest. Markerless tracking of hands and fingers is a promising enabler, but adoption has been hampered because of tracking problems, complex and dense capture setups, high computing requirements, equipment costs, and poor latency. In this paper, we present a method that addresses these issues. Our method tracks rapid and complex articulations of the hand using a single depth camera. It is fast (50 fps without GPU support) and supports varying close-range camera-to-scene arrangements, such as in desktop or egocentric settings, where the camera can even move. We frame pose estimation as an optimization problem in depth using a new objective function based on a collection of Gaussian functions, focusing particularly on robust tracking of finger articulations. We demonstrate the benefits of the method in several interaction applications ranging from manipulating objects in a 3D blocks world to egocentric interaction on the go. We also present extensive evaluation of our method on publicly available datasets which shows that our method achieves competitive accuracy.

Fast Tracking of Hand and Finger Articulations Using a Single Depth Camera

The abundance of mobile devices and digital cameras with video capture makes it easy to obtain large collections of video clips that contain the same location, environment, or event. However, such an unstructured collection is difficult to comprehend and explore. We propose a system that analyzes collections of unstructured but related video data to create a Videoscape: a data structure that enables interactive exploration of video collections by visually navigating – spatially and/or temporally – between different clips. We automatically identify transition opportunities, or portals. From these portals, we construct the Videoscape, a graph whose edges are video clips and whose nodes are portals between clips. Now structured, the videos can be interactively explored by walking the graph or by geographic map. Given this system, we gauge preference for different video transition styles in a user study, and generate heuristics that automatically choose an appropriate transition style. We evaluate our system using three further user studies, which allows us to conclude that Videoscapes provides significant benefits over related methods. Our system leads to previously unseen ways of interactive spatio-temporal exploration of casually captured videos, and we demonstrate this on several video collections.

Videoscapes: Exploring Unstructured Video Collections

Large text corpora with news, customer mail and reports, or Web 2.0 contributions offer a great potential for enhancing business-intelligence applications. We propose a framework for performing text analytics on such data in a versatile, efficient, and scalable manner. While much of the prior literature has emphasized mining keywords or tags in blogs or social-tagging communities, we emphasize the analysis of interesting phrases. These include named entities, important quotations, market slogans, and other multi-word phrases that are prominent in a dynamically derived ad-hoc subset of the corpus, e.g., being frequent in the subset but relatively infrequent in the overall corpus. The ad-hoc subset may be derived by means of a keyword query against the corpus, or by focusing on a particular time period. We investigate alternative definitions of phrase interestingness, based on the probability of phrase occurrences. We develop preprocessing and indexing methods for phrases, paired with new search techniques for the top-k most interesting phrases on ad-hoc subsets of the corpus. Our framework is evaluated using a large-scale real-world corpus of New York Times news articles.

http://domino.mpi-inf.mpg.de/internet/reports.nsf/c125634c000710d0c12560400034f45a/c02e2e11a371e723c125759e00454c3e/$file/mpi-i-2009-5-006.pdf

Jens Dittrich

Papers

Scalable Phrase Mining for Ad-hoc Text Analytics