HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces

Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor search. In this paper, we propose a novel yet simple indexing scheme, HD-Index, to solve the problem of approximate k-nearest neighbor queries in massive high-dimensional databases. HD-Index consists of a set of novel hierarchical structures called RDB-trees built on Hilbert keys of database objects. The leaves of the RDB-trees store distances of database objects to reference objects, thereby allowing efficient pruning using distance filters. In addition to triangular inequality, we also use Ptolemaic inequality to produce better lower bounds. Experiments on massive (up to billion scale) high-dimensional (up to 1000+) datasets show that HD-Index is effective, efficient, and scalable.Comment: PVLDB 11(8):906-919, 201

Reordering Rows for Better Compression: Beyond the Lexicographic Order

Sorting database tables before compressing them improves the compression rate. Can we do better than the lexicographical order? For minimizing the number of runs in a run-length encoding compression scheme, the best approaches to row-ordering are derived from traveling salesman heuristics, although there is a significant trade-off between running time and compression. A new heuristic, Multiple Lists, which is a variant on Nearest Neighbor that trades off compression for a major running-time speedup, is a good option for very large tables. However, for some compression schemes, it is more important to generate long runs rather than few runs. For this case, another novel heuristic, Vortex, is promising. We find that we can improve run-length encoding up to a factor of 3 whereas we can improve prefix coding by up to 80%: these gains are on top of the gains due to lexicographically sorting the table. We prove that the new row reordering is optimal (within 10%) at minimizing the runs of identical values within columns, in a few cases.Comment: to appear in ACM TOD

The True Destination of EGO is Multi-local Optimization

Efficient global optimization is a popular algorithm for the optimization of expensive multimodal black-box functions. One important reason for its popularity is its theoretical foundation of global convergence. However, as the budgets in expensive optimization are very small, the asymptotic properties only play a minor role and the algorithm sometimes comes off badly in experimental comparisons. Many alternative variants have therefore been proposed over the years. In this work, we show experimentally that the algorithm instead has its strength in a setting where multiple optima are to be identified

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Multispectral texture synthesis

Synthesizing texture involves the ordering of pixels in a 2D arrangement so as to display certain known spatial correlations, generally as described by a sample texture. In an abstract sense, these pixels could be gray-scale values, RGB color values, or entire spectral curves. The focus of this work is to develop a practical synthesis framework that maintains this abstract view while synthesizing texture with high spectral dimension, effectively achieving spectral invariance. The principle idea is to use a single monochrome texture synthesis step to capture the spatial information in a multispectral texture. The first step is to use a global color space transform to condense the spatial information in a sample texture into a principle luminance channel. Then, a monochrome texture synthesis step generates the corresponding principle band in the synthetic texture. This spatial information is then used to condition the generation of spectral information. A number of variants of this general approach are introduced. The first uses a multiresolution transform to decompose the spatial information in the principle band into an equivalent scale/space representation. This information is encapsulated into a set of low order statistical constraints that are used to iteratively coerce white noise into the desired texture. The residual spectral information is then generated using a non-parametric Markov Ran dom field model (MRF). The remaining variants use a non-parametric MRF to generate the spatial and spectral components simultaneously. In this ap proach, multispectral texture is grown from a seed region by sampling from the set of nearest neighbors in the sample texture as identified by a template matching procedure in the principle band. The effectiveness of both algorithms is demonstrated on a number of texture examples ranging from greyscale to RGB textures, as well as 16, 22, 32 and 63 band spectral images. In addition to the standard visual test that predominates the literature, effort is made to quantify the accuracy of the synthesis using informative and effective metrics. These include first and second order statistical comparisons as well as statistical divergence tests