Spatial Random Sampling: A Structure-Preserving Data Sketching Tool

Random column sampling is not guaranteed to yield data sketches that preserve the underlying structures of the data and may not sample sufficiently from less-populated data clusters. Also, adaptive sampling can often provide accurate low rank approximations, yet may fall short of producing descriptive data sketches, especially when the cluster centers are linearly dependent. Motivated by that, this paper introduces a novel randomized column sampling tool dubbed Spatial Random Sampling (SRS), in which data points are sampled based on their proximity to randomly sampled points on the unit sphere. The most compelling feature of SRS is that the corresponding probability of sampling from a given data cluster is proportional to the surface area the cluster occupies on the unit sphere, independently from the size of the cluster population. Although it is fully randomized, SRS is shown to provide descriptive and balanced data representations. The proposed idea addresses a pressing need in data science and holds potential to inspire many novel approaches for analysis of big data

Sketch-based subspace clustering of hyperspectral images

Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images

A Distance-preserving Matrix Sketch

Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An important aspect of these methods is how to preserve relative distances between points in the higher-dimensional space after reducing rows and columns to fit in a lower dimensional space. This aspect is important because conclusions based on faulty visual reasoning can be harmful. Judging dissimilar points as similar or similar points as dissimilar on the basis of a visualization can lead to false conclusions. To ameliorate this bias and to make visualizations of very large datasets feasible, we introduce two new algorithms that respectively select a subset of rows and columns of a rectangular matrix. This selection is designed to preserve relative distances as closely as possible. We compare our matrix sketch to more traditional alternatives on a variety of artificial and real datasets.Comment: 38 pages, 13 figure

Streaming histogram sketching for rapid microbiome analytics

Background: The growth in publically available microbiome data in recent years has yielded an invaluable resource for genomic research, allowing for the design of new studies, augmentation of novel datasets and reanalysis of published works. This vast amount of microbiome data, as well as the widespread proliferation of microbiome research and the looming era of clinical metagenomics, means there is an urgent need to develop analytics that can process huge amounts of data in a short amount of time. To address this need, we propose a new method for the compact representation of microbiome sequencing data using similarity-preserving sketches of streaming k-mer spectra. These sketches allow for dissimilarity estimation, rapid microbiome catalogue searching and classification of microbiome samples in near real time. Results: We apply streaming histogram sketching to microbiome samples as a form of dimensionality reduction, creating a compressed ‘histosketch’ that can efficiently represent microbiome k-mer spectra. Using public microbiome datasets, we show that histosketches can be clustered by sample type using the pairwise Jaccard similarity estimation, consequently allowing for rapid microbiome similarity searches via a locality sensitive hashing indexing scheme. Furthermore, we use a ‘real life’ example to show that histosketches can train machine learning classifiers to accurately label microbiome samples. Specifically, using a collection of 108 novel microbiome samples from a cohort of premature neonates, we trained and tested a random forest classifier that could accurately predict whether the neonate had received antibiotic treatment (97% accuracy, 96% precision) and could subsequently be used to classify microbiome data streams in less than 3 s. Conclusions: Our method offers a new approach to rapidly process microbiome data streams, allowing samples to be rapidly clustered, indexed and classified. We also provide our implementation, Histosketching Using Little K-mers (HULK), which can histosketch a typical 2 GB microbiome in 50 s on a standard laptop using four cores, with the sketch occupying 3000 bytes of disk space