PROPAGATE: a seed propagation framework to compute Distance-based metrics on Very Large Graphs

We propose PROPAGATE, a fast approximation framework to estimate distance-based metrics on very large graphs such as the (effective) diameter, the (effective) radius, or the average distance within a small error. The framework assigns seeds to nodes and propagates them in a BFS-like fashion, computing the neighbors set until we obtain either the whole vertex set (the diameter) or a given percentage (the effective diameter). At each iteration, we derive compressed Boolean representations of the neighborhood sets discovered so far. The PROPAGATE framework yields two algorithms: PROPAGATE-P, which propagates all the $s$ seeds in parallel, and PROPAGATE-s which propagates the seeds sequentially. For each node, the compressed representation of the PROPAGATE-P algorithm requires $s$ bits while that of PROPAGATE-S only $1$ bit. Both algorithms compute the average distance, the effective diameter, the diameter, and the connectivity rate within a small error with high probability: for any $\varepsilon>0$ and using $s=\Theta\left(\frac{\log n}{\varepsilon^2}\right)$ sample nodes, the error for the average distance is bounded by $\xi = \frac{\varepsilon \Delta}{\alpha}$, the error for the effective diameter and the diameter are bounded by $\xi = \frac{\varepsilon}{\alpha}$, and the error for the connectivity rate is bounded by $\varepsilon$ where $\Delta$ is the diameter and $\alpha$ is a measure of connectivity of the graph. The time complexity is $\mathcal{O}\left(m\Delta \frac{\log n}{\varepsilon^2}\right)$, where $m$ is the number of edges of the graph. The experimental results show that the PROPAGATE framework improves the current state of the art both in accuracy and speed. Moreover, we experimentally show that PROPAGATE-S is also very efficient for solving the All Pair Shortest Path problem in very large graphs

SUFFIX TREE, MINWISE HASHING AND STREAMING ALGORITHMS FOR BIG DATA ANALYSIS IN BIOINFORMATICS

In this dissertation, we worked on several algorithmic problems in bioinformatics using mainly three approaches: (a) a streaming model, (b) sux-tree based indexing, and (c) minwise-hashing (minhash) and locality-sensitive hashing (LSH). The streaming models are useful for large data problems where a good approximation needs to be achieved with limited space usage. We developed an approximation algorithm (Kmer-Estimate) using the streaming approach to obtain a better estimation of the frequency of k-mer counts. A k-mer, a subsequence of length k, plays an important role in many bioinformatics analyses such as genome distance estimation. We also developed new methods that use sux tree, a trie data structure, for alignment-free, non-pairwise algorithms for a conserved non-coding sequence (CNS) identification problem. We provided two different algorithms: STAG-CNS to identify exact-matched CNSs and DiCE to identify CNSs with mismatches. Using our algorithms, CNSs among various grass species were identified. A different approach was employed for identification of longer CNSs ( 100 bp, mostly found in animals). In our new method (MinCNE), the minhash approach was used to estimate the Jaccard similarity. Using also LSH, k-mers extracted from genomic sequences were clustered and CNSs were identified. Another new algorithm (MinIsoClust) that also uses minhash and LSH techniques was developed for an isoform clustering problem. Isoforms are generated from the same gene but by alternative splicing. As the isoform sequences share some exons but in different combinations, regular sequencing clustering methods do not work well. Our algorithm generates clusters for isoform sequences based on their shared minhash signatures. Finally, we discuss de novo transcriptome assembly algorithms and how to improve the assembly accuracy using ensemble approaches. First, we did a comprehensive performance analysis on different transcriptome assemblers using simulated benchmark datasets. Then, we developed a new ensemble approach (Minsemble) for the de novo transcriptome assembly problem that integrates isoform-clustering using minhash technique to identify potentially correct transcripts from various de novo transcriptome assemblers. Minsemble identified more correctly assembled transcripts as well as genes compared to other de novo and ensemble methods. Adviser: Jitender S. Deogu

DotHash: Estimating Set Similarity Metrics for Link Prediction and Document Deduplication

Metrics for set similarity are a core aspect of several data mining tasks. To remove duplicate results in a Web search, for example, a common approach looks at the Jaccard index between all pairs of pages. In social network analysis, a much-celebrated metric is the Adamic-Adar index, widely used to compare node neighborhood sets in the important problem of predicting links. However, with the increasing amount of data to be processed, calculating the exact similarity between all pairs can be intractable. The challenge of working at this scale has motivated research into efficient estimators for set similarity metrics. The two most popular estimators, MinHash and SimHash, are indeed used in applications such as document deduplication and recommender systems where large volumes of data need to be processed. Given the importance of these tasks, the demand for advancing estimators is evident. We propose DotHash, an unbiased estimator for the intersection size of two sets. DotHash can be used to estimate the Jaccard index and, to the best of our knowledge, is the first method that can also estimate the Adamic-Adar index and a family of related metrics. We formally define this family of metrics, provide theoretical bounds on the probability of estimate errors, and analyze its empirical performance. Our experimental results indicate that DotHash is more accurate than the other estimators in link prediction and detecting duplicate documents with the same complexity and similar comparison time

Applied Randomized Algorithms for Efficient Genomic Analysis

The scope and scale of biological data continues to grow at an exponential clip, driven by advances in genetic sequencing, annotation and widespread adoption of surveillance efforts. For instance, the Sequence Read Archive (SRA) now contains more than 25 petabases of public data, while RefSeq, a collection of reference genomes, recently surpassed 100,000 complete genomes. In the process, it has outgrown the practical reach of many traditional algorithmic approaches in both time and space. Motivated by this extreme scale, this thesis details efficient methods for clustering and summarizing large collections of sequence data. While our primary area of interest is biological sequences, these approaches largely apply to sequence collections of any type, including natural language, software source code, and graph structured data. We applied recent advances in randomized algorithms to practical problems. We used MinHash and HyperLogLog, both examples of Locality- Sensitive Hashing, as well as coresets, which are approximate representations for finite sum problems, to build methods capable of scaling to billions of items. Ultimately, these are all derived from variations on sampling. We combined these advances with hardware-based optimizations and incorporated into free and open-source software libraries (sketch, frp, lib- simdsampling) and practical software tools built on these libraries (Dashing, Minicore, Dashing 2), empowering users to interact practically with colossal datasets on commodity hardware

NEMA: Automatic Integration of Large Network Management Databases

Network management, whether for malfunction analysis, failure prediction, performance monitoring and improvement, generally involves large amounts of data from different sources. To effectively integrate and manage these sources, automatically finding semantic matches among their schemas or ontologies is crucial. Existing approaches on database matching mainly fall into two categories. One focuses on the schema-level matching based on schema properties such as field names, data types, constraints and schema structures. Network management databases contain massive tables (e.g., network products, incidents, security alert and logs) from different departments and groups with nonuniform field names and schema characteristics. It is not reliable to match them by those schema properties. The other category is based on the instance-level matching using general string similarity techniques, which are not applicable for the matching of large network management databases. In this paper, we develop a matching technique for large NEtwork MAnagement databases (NEMA) deploying instance-level matching for effective data integration and connection. We design matching metrics and scores for both numerical and non-numerical fields and propose algorithms for matching these fields. The effectiveness and efficiency of NEMA are evaluated by conducting experiments based on ground truth field pairs in large network management databases. Our measurement on large databases with 1,458 fields, each of which contains over 10 million records, reveals that NEMA can achieve accuracy of 95%. We further compare with several other existing algorithms, and show that NEMA outperforms them by 7%-15% in numerical matching and achieves the best trade-off for non-numerical matching

Differentially Private One Permutation Hashing and Bin-wise Consistent Weighted Sampling

Minwise hashing (MinHash) is a standard algorithm widely used in the industry, for large-scale search and learning applications with the binary (0/1) Jaccard similarity. One common use of MinHash is for processing massive n-gram text representations so that practitioners do not have to materialize the original data (which would be prohibitive). Another popular use of MinHash is for building hash tables to enable sub-linear time approximate near neighbor (ANN) search. MinHash has also been used as a tool for building large-scale machine learning systems. The standard implementation of MinHash requires applying $K$ random permutations. In comparison, the method of one permutation hashing (OPH), is an efficient alternative of MinHash which splits the data vectors into $K$ bins and generates hash values within each bin. OPH is substantially more efficient and also more convenient to use. In this paper, we combine the differential privacy (DP) with OPH (as well as MinHash), to propose the DP-OPH framework with three variants: DP-OPH-fix, DP-OPH-re and DP-OPH-rand, depending on which densification strategy is adopted to deal with empty bins in OPH. A detailed roadmap to the algorithm design is presented along with the privacy analysis. An analytical comparison of our proposed DP-OPH methods with the DP minwise hashing (DP-MH) is provided to justify the advantage of DP-OPH. Experiments on similarity search confirm the merits of DP-OPH, and guide the choice of the proper variant in different practical scenarios. Our technique is also extended to bin-wise consistent weighted sampling (BCWS) to develop a new DP algorithm called DP-BCWS for non-binary data. Experiments on classification tasks demonstrate that DP-BCWS is able to achieve excellent utility at around $\epsilon = 5\sim 10$, where $\epsilon$ is the standard parameter in the language of $(\epsilon, \delta)$-DP

Top-K Queries Over Digital Traces

Recent advances in social and mobile technology have enabled an abundance of digital traces (in the form of mobile check-ins, WiFi hotspots handshaking, etc.) revealing the physical presence history of diverse sets of entities. One challenging, yet important, task is to identify k entities that are most closely associated with a given query entity based on their digital traces. We propose a suite of hierarchical indexing techniques and algorithms to enable fast query processing for this problem at scale. We theoretically analyze the pruning effectiveness of the proposed methods based on a human mobility model which we propose and validate in real life situations. Finally, we conduct extensive experiments on both synthetic and real datasets at scale, evaluating the performance of our techniques, confirming the effectiveness and superiority of our approach over other applicable approaches across a variety of parameter settings and datasets