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

Space-efficient data sketching algorithms for network applications

Sketching techniques are widely adopted in network applications. Sketching algorithms “encode” data into succinct data structures that can later be accessed and “decoded” for various purposes, such as network measurement, accounting, anomaly detection and etc. Bloom filters and counter braids are two well-known representatives in this category. Those sketching algorithms usually need to strike a tradeoff between performance (how much information can be revealed and how fast) and cost (storage, transmission and computation). This dissertation is dedicated to the research and development of several sketching techniques including improved forms of stateful Bloom Filters, Statistical Counter Arrays and Error Estimating Codes. Bloom filter is a space-efficient randomized data structure for approximately representing a set in order to support membership queries. Bloom filter and its variants have found widespread use in many networking applications, where it is important to minimize the cost of storing and communicating network data. In this thesis, we propose a family of Bloom Filter variants augmented by rank-indexing method. We will show such augmentation can bring a significant reduction of space and also the number of memory accesses, especially when deletions of set elements from the Bloom Filter need to be supported. Exact active counter array is another important building block in many sketching algorithms, where storage cost of the array is of paramount concern. Previous approaches reduce the storage costs while either losing accuracy or supporting only passive measurements. In this thesis, we propose an exact statistics counter array architecture that can support active measurements (real-time read and write). It also leverages the aforementioned rank-indexing method and exploits statistical multiplexing to minimize the storage costs of the counter array. Error estimating coding (EEC) has recently been established as an important tool to estimate bit error rates in the transmission of packets over wireless links. In essence, the EEC problem is also a sketching problem, since the EEC codes can be viewed as a sketch of the packet sent, which is decoded by the receiver to estimate bit error rate. In this thesis, we will first investigate the asymptotic bound of error estimating coding by viewing the problem from two-party computation perspective and then investigate its coding/decoding efficiency using Fisher information analysis. Further, we develop several sketching techniques including Enhanced tug-of-war(EToW) sketch and the generalized EEC (gEEC)sketch family which can achieve around 70% reduction of sketch size with similar estimation accuracies. For all solutions proposed above, we will use theoretical tools such as information theory and communication complexity to investigate how far our proposed solutions are away from the theoretical optimal. We will show that the proposed techniques are asymptotically or empirically very close to the theoretical bounds.PhDCommittee Chair: Xu, Jun; Committee Member: Feamster, Nick; Committee Member: Li, Baochun; Committee Member: Romberg, Justin; Committee Member: Zegura, Ellen W

Randomized Robust Subspace Recovery for High Dimensional Data Matrices

This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low dimensional embedding, while in the other, sketching is based on random column and row sampling. Both designs are shown to bring about substantial savings in complexity and memory requirements for robust subspace learning over conventional approaches that use the full scale data. A characterization of the sample and computational complexity of both designs is derived in the context of two distinct outlier models, namely, sparse and independent outlier models. The proposed randomized approach can provably recover the correct subspace with computational and sample complexity that are almost independent of the size of the data. The results of the mathematical analysis are confirmed through numerical simulations using both synthetic and real data

Fractional Hitting Sets for Efficient and Lightweight Genomic Data Sketching

The exponential increase in publicly available sequencing data and genomic resources necessitates the development of highly efficient methods for data processing and analysis. Locality-sensitive hashing techniques have successfully transformed large datasets into smaller, more manageable sketches while maintaining comparability using metrics such as Jaccard and containment indices. However, fixed-size sketches encounter difficulties when applied to divergent datasets. Scalable sketching methods, such as Sourmash, provide valuable solutions but still lack resource-efficient, tailored indexing. Our objective is to create lighter sketches with comparable results while enhancing efficiency. We introduce the concept of Fractional Hitting Sets, a generalization of Universal Hitting Sets, which uniformly cover a specified fraction of the k-mer space. In theory and practice, we demonstrate the feasibility of achieving such coverage with simple but highly efficient schemes. By encoding the covered k-mers as super-k-mers, we provide a space-efficient exact representation that also enables optimized comparisons. Our novel tool, SuperSampler, implements this scheme, and experimental results with real bacterial collections closely match our theoretical findings. In comparison to Sourmash, SuperSampler achieves similar outcomes while utilizing an order of magnitude less space and memory and operating several times faster. This highlights the potential of our approach in addressing the challenges presented by the ever-expanding landscape of genomic data

Fast Similarity Graph Construction via Data Sketching Techniques

Graphs are mathematical structures used to model objects and their pairwise relationships. Due to their simple but expressive abstract representation, they are commonly used to model various types of relations and processes in technological, social or biological systems and have found numerous applications. A special type of graph is the similarity graph in which nodes represent entities and there is an edge connecting two nodes if the two entities are similar based on some similarity measure. In a typical scenario, raw data of entities are provided in the form of a relational dataset, matrix or a tensor and a similarity graph is built to facilitate graph-based analysis like node importance, node classification, link prediction, community detection, outlier detection, and more. The ability to construct similarity graphs fast is important and with a potential for high impact, thus several approximation techniques have been proposed. In this work, we propose data sketching based methods for fast approximate similarity graph construction. Data sketching techniques are applied on the raw data and are designed to achieve desired error guarantees. They can drastically reduce the size of raw data on which we operate, allowing for faster construction and analysis of similarity graphs, but with approximate results. This is a desirable tradeoff for many applications in diverse domains. Through a thorough experimental evaluation, we demonstrate that our sketching methods outperform sensible baselines and competitor methods proposed for the problem. First, they are much faster than exact methods while maintaining high accuracy in constructing the similarity graph. Furthermore, our methods demonstrate significantly higher accuracy than competitive methods on generic graph analysis tasks. We demonstrate the effectiveness of our methods on different real-world graph applications