Using treemaps for variable selection in spatio-temporal visualisation

We demonstrate and reflect upon the use of enhanced treemaps that incorporate spatial and temporal ordering for exploring a large multivariate spatio-temporal data set. The resulting data-dense views summarise and simultaneously present hundreds of space-, time-, and variable-constrained subsets of a large multivariate data set in a structure that facilitates their meaningful comparison and supports visual analysis. Interactive techniques allow localised patterns to be explored and subsets of interest selected and compared with the spatial aggregate. Spatial variation is considered through interactive raster maps and high-resolution local road maps. The techniques are developed in the context of 42.2 million records of vehicular activity in a 98 km(2) area of central London and informally evaluated through a design used in the exploratory visualisation of this data set. The main advantages of our technique are the means to simultaneously display hundreds of summaries of the data and to interactively browse hundreds of variable combinations with ordering and symbolism that are consistent and appropriate for space- and time- based variables. These capabilities are difficult to achieve in the case of spatio-temporal data with categorical attributes using existing geovisualisation methods. We acknowledge limitations in the treemap representation but enhance the cognitive plausibility of this popular layout through our two-dimensional ordering algorithm and interactions. Patterns that are expected (e.g. more traffic in central London), interesting (e.g. the spatial and temporal distribution of particular vehicle types) and anomalous (e.g. low speeds on particular road sections) are detected at various scales and locations using the approach. In many cases, anomalies identify biases that may have implications for future use of the data set for analyses and applications. Ordered treemaps appear to have potential as interactive interfaces for variable selection in spatio-temporal visualisation. Information Visualization (2008) 7, 210-224. doi: 10.1057/palgrave.ivs.950018

Forecasting the cost of processing multi-join queries via hashing for main-memory databases (Extended version)

Database management systems (DBMSs) carefully optimize complex multi-join queries to avoid expensive disk I/O. As servers today feature tens or hundreds of gigabytes of RAM, a significant fraction of many analytic databases becomes memory-resident. Even after careful tuning for an in-memory environment, a linear disk I/O model such as the one implemented in PostgreSQL may make query response time predictions that are up to 2X slower than the optimal multi-join query plan over memory-resident data. This paper introduces a memory I/O cost model to identify good evaluation strategies for complex query plans with multiple hash-based equi-joins over memory-resident data. The proposed cost model is carefully validated for accuracy using three different systems, including an Amazon EC2 instance, to control for hardware-specific differences. Prior work in parallel query evaluation has advocated right-deep and bushy trees for multi-join queries due to their greater parallelization and pipelining potential. A surprising finding is that the conventional wisdom from shared-nothing disk-based systems does not directly apply to the modern shared-everything memory hierarchy. As corroborated by our model, the performance gap between the optimal left-deep and right-deep query plan can grow to about 10X as the number of joins in the query increases.Comment: 15 pages, 8 figures, extended version of the paper to appear in SoCC'1

Finding Associations and Computing Similarity via Biased Pair Sampling

This version is ***superseded*** by a full version that can be found at http://www.itu.dk/people/pagh/papers/mining-jour.pdf, which contains stronger theoretical results and fixes a mistake in the reporting of experiments. Abstract: Sampling-based methods have previously been proposed for the problem of finding interesting associations in data, even for low-support items. While these methods do not guarantee precise results, they can be vastly more efficient than approaches that rely on exact counting. However, for many similarity measures no such methods have been known. In this paper we show how a wide variety of measures can be supported by a simple biased sampling method. The method also extends to find high-confidence association rules. We demonstrate theoretically that our method is superior to exact methods when the threshold for "interesting similarity/confidence" is above the average pairwise similarity/confidence, and the average support is not too low. Our method is particularly good when transactions contain many items. We confirm in experiments on standard association mining benchmarks that this gives a significant speedup on real data sets (sometimes much larger than the theoretical guarantees). Reductions in computation time of over an order of magnitude, and significant savings in space, are observed.Comment: This is an extended version of a paper that appeared at the IEEE International Conference on Data Mining, 2009. The conference version is (c) 2009 IEE

Metric learning pairwise kernel for graph inference

Much recent work in bioinformatics has focused on the inference of various types of biological networks, representing gene regulation, metabolic processes, protein-protein interactions, etc. A common setting involves inferring network edges in a supervised fashion from a set of high-confidence edges, possibly characterized by multiple, heterogeneous data sets (protein sequence, gene expression, etc.). Here, we distinguish between two modes of inference in this setting: direct inference based upon similarities between nodes joined by an edge, and indirect inference based upon similarities between one pair of nodes and another pair of nodes. We propose a supervised approach for the direct case by translating it into a distance metric learning problem. A relaxation of the resulting convex optimization problem leads to the support vector machine (SVM) algorithm with a particular kernel for pairs, which we call the metric learning pairwise kernel (MLPK). We demonstrate, using several real biological networks, that this direct approach often improves upon the state-of-the-art SVM for indirect inference with the tensor product pairwise kernel