Real-time analytics on large dynamic graphs

In today's fast-paced and interconnected digital world, the data generated by an increasing number of applications is being modeled as dynamic graphs. The graph structure encodes relationships among data items, while the structural changes to the graphs as well as the continuous stream of information produced by the entities in these graphs make them dynamic in nature. Examples include social networks where users post status updates, images, videos, etc.; phone call networks where nodes may send text messages or place phone calls; road traffic networks where the traffic behavior of the road segments changes constantly, and so on. There is a tremendous value in storing, managing, and analyzing such dynamic graphs and deriving meaningful insights in real-time. However, a majority of the work in graph analytics assumes a static setting, and there is a lack of systematic study of the various dynamic scenarios, the complexity they impose on the analysis tasks, and the challenges in building efficient systems that can support such tasks at a large scale. In this dissertation, I design a unified streaming graph data management framework, and develop prototype systems to support increasingly complex tasks on dynamic graphs. In the first part, I focus on the management and querying of distributed graph data. I develop a hybrid replication policy that monitors the read-write frequencies of the nodes to decide dynamically what data to replicate, and whether to do eager or lazy replication in order to minimize network communication and support low-latency querying. In the second part, I study parallel execution of continuous neighborhood-driven aggregates, where each node aggregates the information generated in its neighborhoods. I build my system around the notion of an aggregation overlay graph, a pre-compiled data structure that enables sharing of partial aggregates across different queries, and also allows partial pre-computation of the aggregates to minimize the query latencies and increase throughput. Finally, I extend the framework to support continuous detection and analysis of activity-based subgraphs, where subgraphs could be specified using both graph structure as well as activity conditions on the nodes. The query specification tasks in my system are expressed using a set of active structural primitives, which allows the query evaluator to use a set of novel optimization techniques, thereby achieving high throughput. Overall, in this dissertation, I define and investigate a set of novel tasks on dynamic graphs, design scalable optimization techniques, build prototype systems, and show the effectiveness of the proposed techniques through extensive evaluation using large-scale real and synthetic datasets.

Probabilistic Models for Scalable Knowledge Graph Construction

In the past decade, systems that extract information from millions of Internet documents have become commonplace. Knowledge graphs -- structured knowledge bases that describe entities, their attributes and the relationships between them -- are a powerful tool for understanding and organizing this vast amount of information. However, a significant obstacle to knowledge graph construction is the unreliability of the extracted information, due to noise and ambiguity in the underlying data or errors made by the extraction system and the complexity of reasoning about the dependencies between these noisy extractions. My dissertation addresses these challenges by exploiting the interdependencies between facts to improve the quality of the knowledge graph in a scalable framework. I introduce a new approach called knowledge graph identification (KGI), which resolves the entities, attributes and relationships in the knowledge graph by incorporating uncertain extractions from multiple sources, entity co-references, and ontological constraints. I define a probability distribution over possible knowledge graphs and infer the most probable knowledge graph using a combination of probabilistic and logical reasoning. Such probabilistic models are frequently dismissed due to scalability concerns, but my implementation of KGI maintains tractable performance on large problems through the use of hinge-loss Markov random fields, which have a convex inference objective. This allows the inference of large knowledge graphs using 4M facts and 20M ground constraints in 2 hours. To further scale the solution, I develop a distributed approach to the KGI problem which runs in parallel across multiple machines, reducing inference time by 90%. Finally, I extend my model to the streaming setting, where a knowledge graph is continuously updated by incorporating newly extracted facts. I devise a general approach for approximately updating inference in convex probabilistic models, and quantify the approximation error by defining and bounding inference regret for online models. Together, my work retains the attractive features of probabilistic models while providing the scalability necessary for large-scale knowledge graph construction. These models have been applied on a number of real-world knowledge graph projects, including the NELL project at Carnegie Mellon and the Google Knowledge Graph.

Expedition in Data and Harmonic Analysis on Graphs

The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-frequency operators have been defined on graphs using Laplacian eigenvalues and eigenvectors. We extend these results and prove that the translation operator to the i’th node is invertible if and only if all eigenvectors are nonzero on the i’th node. Because of this dependency on the support of eigenvectors we study the characteristic set of Laplacian eigenvectors. We prove that the Fiedler vector of a planar graph cannot vanish on large neighborhoods and then explicitly construct a family of non-planar graphs that do exhibit this property. We then prove original results in modern analysis on graphs. We extend results on spectral graph wavelets to create vertex-dyanamic spectral graph wavelets whose support depends on both scale and translation parameters. We prove that Spielman’s Twice-Ramanujan graph sparsifying algorithm cannot outperform his conjectured optimal sparsification constant. Finally, we present numerical results on graph conditioning, in which edges of a graph are rescaled to best approximate the complete graph and reduce average commute time.

BUILDING EFFICIENT AND COST-EFFECTIVE CLOUD-BASED BIG DATA MANAGEMENT SYSTEMS

In today’s big data world, data is being produced in massive volumes, at great velocity and from a variety of different sources such as mobile devices, sensors, a plethora of small devices hooked to the internet (Internet of Things), social networks, communication networks and many others. Interactive querying and large-scale analytics are being increasingly used to derive value out of this big data. A large portion of this data is being stored and processed in the Cloud due the several advantages provided by the Cloud such as scalability, elasticity, availability, low cost of ownership and the overall economies of scale. There is thus, a growing need for large-scale cloud-based data management systems that can support real-time ingest, storage and processing of large volumes of heterogeneous data. However, in the pay-as-you-go Cloud environment, the cost of analytics can grow linearly with the time and resources required. Reducing the cost of data analytics in the Cloud thus remains a primary challenge. In my dissertation research, I have focused on building efficient and cost-effective cloud-based data management systems for different application domains that are predominant in cloud computing environments. In the first part of my dissertation, I address the problem of reducing the cost of transactional workloads on relational databases to support database-as-a-service in the Cloud. The primary challenges in supporting such workloads include choosing how to partition the data across a large number of machines, minimizing the number of distributed transactions, providing high data availability, and tolerating failures gracefully. I have designed, built and evaluated SWORD, an end-to-end scalable online transaction processing system, that utilizes workload-aware data placement and replication to minimize the number of distributed transactions that incorporates a suite of novel techniques to significantly reduce the overheads incurred both during the initial placement of data, and during query execution at runtime. In the second part of my dissertation, I focus on sampling-based progressive analytics as a means to reduce the cost of data analytics in the relational domain. Sampling has been traditionally used by data scientists to get progressive answers to complex analytical tasks over large volumes of data. Typically, this involves manually extracting samples of increasing data size (progressive samples) for exploratory querying. This provides the data scientists with user control, repeatable semantics, and result provenance. However, such solutions result in tedious workflows that preclude the reuse of work across samples. On the other hand, existing approximate query processing systems report early results, but do not offer the above benefits for complex ad-hoc queries. I propose a new progressive data-parallel computation framework, NOW!, that provides support for progressive analytics over big data. In particular, NOW! enables progressive relational (SQL) query support in the Cloud using unique progress semantics that allow efficient and deterministic query processing over samples providing meaningful early results and provenance to data scientists. NOW! enables the provision of early results using significantly fewer resources thereby enabling a substantial reduction in the cost incurred during such analytics. Finally, I propose NSCALE, a system for efficient and cost-effective complex analytics on large-scale graph-structured data in the Cloud. The system is based on the key observation that a wide range of complex analysis tasks over graph data require processing and reasoning about a large number of multi-hop neighborhoods or subgraphs in the graph; examples include ego network analysis, motif counting in biological networks, finding social circles in social networks, personalized recommendations, link prediction, etc. These tasks are not well served by existing vertex-centric graph processing frameworks whose computation and execution models limit the user program to directly access the state of a single vertex, resulting in high execution overheads. Further, the lack of support for extracting the relevant portions of the graph that are of interest to an analysis task and loading it onto distributed memory leads to poor scalability. NSCALE allows users to write programs at the level of neighborhoods or subgraphs rather than at the level of vertices, and to declaratively specify the subgraphs of interest. It enables the efficient distributed execution of these neighborhood-centric complex analysis tasks over largescale graphs, while minimizing resource consumption and communication cost, thereby substantially reducing the overall cost of graph data analytics in the Cloud. The results of our extensive experimental evaluation of these prototypes with several real-world data sets and applications validate the effectiveness of our techniques which provide orders-of-magnitude reductions in the overheads of distributed data querying and analysis in the Cloud.

Leveraging Multiple Features for Image Retrieval and Matching

The goal of image retrieval and matching is to find and locate object instances in images from a large-scale image database. While visual features are abundant, how to combine them to improve performance by individual features remains a challenging task. In this work, we focus on leveraging multiple features for accurate and efficient image retrieval and matching. We first propose two graph-based approaches to rerank initially retrieved images for generic image retrieval. In the graph, vertices are images while edges are similarities between image pairs. Our first approach employs a mixture Markov model based on a random walk model on multiple graphs to fuse graphs. We introduce a probabilistic model to compute the importance of each feature for graph fusion under a naive Bayesian formulation, which requires statistics of similarities from a manually labeled dataset containing irrelevant images. To reduce human labeling, we further propose a fully unsupervised reranking algorithm based on a submodular objective function that can be efficiently optimized by greedy algorithm. By maximizing an information gain term over the graph, our submodular function favors a subset of database images that are similar to query images and resemble each other. The function also exploits the rank relationships of images from multiple ranked lists obtained by different features. We then study a more well-defined application, person re-identification, where the database contains labeled images of human bodies captured by multiple cameras. Re-identifications from multiple cameras are regarded as related tasks to exploit shared information. We apply a novel multi-task learning algorithm using both low level features and attributes. A low rank attribute embedding is joint learned within the multi-task learning formulation to embed original binary attributes to a continuous attribute space, where incorrect and incomplete attributes are rectified and recovered. To locate objects in images, we design an object detector based on object proposals and deep convolutional neural networks (CNN) in view of the emergence of deep networks. We improve a Fast RCNN framework and investigate two new strategies to detect objects accurately and efficiently: scale-dependent pooling (SDP) and cascaded rejection classifiers (CRC). The SDP improves detection accuracy by exploiting appropriate convolutional features depending on the scale of input object proposals. The CRC effectively utilizes convolutional features and greatly eliminates negative proposals in a cascaded manner, while maintaining a high recall for true objects. The two strategies together improve the detection accuracy and reduce the computational cost.

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.