Histosketch: fast similarity-preserving sketching of streaming histograms with concept drift

Histogram-based similarity has been widely adopted in many machine learning tasks. However, measuring histogram similarity is a challenging task for streaming data, where the elements of a histogram are observed in a streaming manner. First, the ever-growing cardinality of histogram elements makes any similarity computation inefficient. Second, the concept-drift issue in the data streams also impairs the accurate assessment of the similarity. In this paper, we propose to overcome the above challenges with HistoSketch, a fast similarity-preserving sketching method for streaming histograms with concept drift. Specifically, HistoSketch is designed to incrementally maintain a set of compact and fixed-size sketches of streaming histograms to approximate similarity between the histograms, with the special consideration of gradually forgetting the outdated histogram elements. We evaluate HistoSketch on multiple classification tasks using both synthetic and real-world datasets. The results show that our method is able to efficiently approximate similarity for streaming histograms and quickly adapt to concept drift. Compared to full streaming histograms gradually forgetting the outdated histogram elements, HistoSketch is able to dramatically reduce the classification time (with a 7500x speedup) with only a modest loss in accuracy (about 3.5%)

Approximating Properties of Data Streams

In this dissertation, we present algorithms that approximate properties in the data stream model, where elements of an underlying data set arrive sequentially, but algorithms must use space sublinear in the size of the underlying data set. We first study the problem of finding all k-periods of a length-n string S, presented as a data stream. S is said to have k-period p if its prefix of length n − p differs from its suffix of length n − p in at most k locations. We give algorithms to compute the k-periods of a string S using poly(k, log n) bits of space and we complement these results with comparable lower bounds. We then study the problem of identifying a longest substring of strings S and T of length n that forms a d-near-alignment under the edit distance, in the simultaneous streaming model. In this model, symbols of strings S and T are streamed at the same time and form a d-near-alignment if the distance between them in some given metric is at most d. We give several algorithms, including an exact one-pass algorithm that uses O(d2 + d log n) bits of space. We then consider the distinct elements and `p-heavy hitters problems in the sliding window model, where only the most recent n elements in the data stream form the underlying set. We first introduce the composable histogram, a simple twist on the exponential (Datar et al., SODA 2002) and smooth histograms (Braverman and Ostrovsky, FOCS 2007) that may be of independent interest. We then show that the composable histogram along with a careful combination of existing techniques to track either the identity or frequency of a few specific items suffices to obtain algorithms for both distinct elements and `p-heavy hitters that is nearly optimal in both n and c. Finally, we consider the problem of estimating the maximum weighted matching of a graph whose edges are revealed in a streaming fashion. We develop a reduction from the maximum weighted matching problem to the maximum cardinality matching problem that only doubles the approximation factor of a streaming algorithm developed for the maximum cardinality matching problem. As an application, we obtain an estimator for the weight of a maximum weighted matching in bounded-arboricity graphs and in particular, a (48 + )-approximation estimator for the weight of a maximum weighted matching in planar graphs

D2 histosketch: discriminative and dynamic similarity-preserving sketching of streaming histograms

Histogram-based similarity has been widely adopted in many machine learning tasks. However, measuring histogram similarity is a challenging task for streaming histograms, where the elements of a histogram are observed one after the other in an online manner. The ever-growing cardinality of histogram elements over the data streams makes any similarity computation inefficient in that case. To tackle this problem, we propose in this paper D2HistoSketch, a similarity-preserving sketching method for streaming histograms to efficiently approximate their Discriminative and Dynamic similarity. D2HistoSketch can fast and memory-efficiently maintain a set of compact and fixed-size sketches of streaming histograms to approximate the similarity between histograms. To provide high-quality similarity approximations, D2HistoSketch considers both discriminative and gradual forgetting weights for similarity measurement, and seamlessly incorporates them in the sketches. Based on both synthetic and real-world datasets, our empirical evaluation shows that our method is able to efficiently and effectively approximate the similarity between streaming histograms while outperforming state-of-the-art sketching methods. Compared to full streaming histograms with both discriminative and gradual forgetting weights in particular, D2HistoSketch is able to dramatically reduce the classification time (with a 7500x speedup) at the expense of a small loss in accuracy only (about 3.25%)

Anomaly Detection in Network Streams Through a Distributional Lens

Anomaly detection in computer networks yields valuable information on events relating to the components of a network, their states, the users in a network and their activities. This thesis provides a unified distribution-based methodology for online detection of anomalies in network traffic streams. The methodology is distribution-based in that it regards the traffic stream as a time series of distributions (histograms), and monitors metrics of distributions in the time series. The effectiveness of the methodology is demonstrated in three application scenarios. First, in 802.11 wireless traffic, we show the ability to detect certain classes of attacks using the methodology. Second, in information network update streams (specifically in Wikipedia) we show the ability to detect the activity of bots, flash events, and outages, as they occur. Third, in Voice over IP traffic streams, we show the ability to detect covert channels that exfiltrate confidential information out of the network. Our experiments show the high detection rate of the methodology when compared to other existing methods, while maintaining a low rate of false positives. Furthermore, we provide algorithmic results that enable efficient and scalable implementation of the above methodology, to accomodate the massive data rates observed in modern infomation streams on the Internet. Through these applications, we present an extensive study of several aspects of the methodology. We analyze the behavior of metrics we consider, providing justification of our choice of those metrics, and how they can be used to diagnose anomalies. We provide insight into the choice of parameters, like window length and threshold, used in anomaly detection

Streaming Algorithms Via Reductions

In the streaming algorithms model of computation we must process data in order and without enough memory to remember the entire input. We study reductions between problems in the streaming model with an eye to using reductions as an algorithm design technique. Our contributions include: * Linear Transformation reductions, which compose with existing linear sketch techniques. We use these for small-space algorithms for numeric measurements of distance-from-periodicity, finding the period of a numeric stream, and detecting cyclic shifts. * The first streaming graph algorithms in the sliding window\u27 model, where we must consider only the most recent L elements for some fixed threshold L. We develop basic algorithms for connectivity and unweighted maximum matching, then develop a variety of other algorithms via reductions to these problems. * A new reduction from maximum weighted matching to maximum unweighted matching. This reduction immediately yields improved approximation guarantees for maximum weighted matching in the semistreaming, sliding window, and MapReduce models, and extends to the more general problem of finding maximum independent sets in p-systems. * Algorithms in a stream-of-samples model which exhibit clear sample vs. space tradeoffs. These algorithms are also inspired by examining reductions. We provide algorithms for calculating F_k frequency moments and graph connectivity

Algorithmic Techniques for Processing Data Streams

We give a survey at some algorithmic techniques for processing data streams. After covering the basic methods of sampling and sketching, we present more evolved procedures that resort on those basic ones. In particular, we examine algorithmic schemes for similarity mining, the concept of group testing, and techniques for clustering and summarizing data streams

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

Interactive Visual Analysis of Process Data

Data gathered from processes, or process data, contains many different aspects that a visualization system should also convey. Aspects such as, temporal coherence, spatial connectivity, streaming data, and the need for in-situ visualizations, which all come with their independent challenges. Additionally, as sensors get more affordable, and the benefits of measurements get clearer we are faced with a deluge of data, of which sizes are rapidly growing. With all the aspects that should be supported and the vast increase in the amount of data, the traditional techniques of dashboards showing the recent data becomes insufficient for practical use. In this thesis we investigate how to extend the traditional process visualization techniques by bringing the streaming process data into an interactive visual analysis setting. The augmentation of process visualization with interactivity enables the users to go beyond the mere observation, pose questions about observed phenomena and delve into the data to mine for the answers. Furthermore, this thesis investigates how to utilize frequency based, as opposed to item based, techniques to show such large amounts of data. By utilizing Kernel Density Estimates (KDE) we show how the display of streaming data benefit by the non-parametric automatic aggregation to interpret incoming data put in context to historic data