Design and analysis of algorithms for similarity search based on intrinsic dimension

One of the most fundamental operations employed in data mining tasks such as classification, cluster analysis, and anomaly detection, is that of similarity search. It has been used in numerous fields of application such as multimedia, information retrieval, recommender systems and pattern recognition. Specifically, a similarity query aims to retrieve from the database the most similar objects to a query object, where the underlying similarity measure is usually expressed as a distance function. The cost of processing similarity queries has been typically assessed in terms of the representational dimension of the data involved, that is, the number of features used to represent individual data objects. It is generally the case that high representational dimension would result in a significant increase in the processing cost of similarity queries. This relation is often attributed to an amalgamation of phenomena, collectively referred to as the curse of dimensionality. However, the observed effects of dimensionality in practice may not be as severe as expected. This has led to the development of models quantifying the complexity of data in terms of some measure of the intrinsic dimensionality. The generalized expansion dimension (GED) is one of such models, which estimates the intrinsic dimension in the vicinity of a query point q through the observation of the ranks and distances of pairs of neighbors with respect to q. This dissertation is mainly concerned with the design and analysis of search algorithms, based on the GED model. In particular, three variants of similarity search problem are considered, including adaptive similarity search, flexible aggregate similarity search, and subspace similarity search. The good practical performance of the proposed algorithms demonstrates the effectiveness of dimensionality-driven design of search algorithms

M-Grid : A distributed framework for multidimensional indexing and querying of location based big data

The widespread use of mobile devices and the real time availability of user-location information is facilitating the development of new personalized, location-based applications and services (LBSs). Such applications require multi-attribute query processing, handling of high access scalability, support for millions of users, real time querying capability and analysis of large volumes of data. Cloud computing aided a new generation of distributed databases commonly known as key-value stores. Key-value stores were designed to extract value from very large volumes of data while being highly available, fault-tolerant and scalable, hence providing much needed features to support LBSs. However complex queries on multidimensional data cannot be processed efficiently as they do not provide means to access multiple attributes. In this thesis we present MGrid, a unifying indexing framework which enables key-value stores to support multidimensional queries. We organize a set of nodes in a P-Grid overlay network which provides fault-tolerance and efficient query processing. We use Hilbert Space Filling Curve based linearization technique which preserves the data locality to efficiently manage multi-dimensional data in a key-value store. We propose algorithms to dynamically process range and k nearest neighbor (kNN) queries on linearized values. This removes the overhead of maintaining a separate index table. Our approach is completely independent from the underlying storage layer and can be implemented on any cloud infrastructure. Experiments on Amazon EC2 show that MGrid achieves a performance improvement of three orders of magnitude in comparison to MapReduce and four times to that of MDHBase scheme --Abstract, pages iii-iv

Scalable aggregation predictive analytics: a query-driven machine learning approach

We introduce a predictive modeling solution that provides high quality predictive analytics over aggregation queries in Big Data environments. Our predictive methodology is generally applicable in environments in which large-scale data owners may or may not restrict access to their data and allow only aggregation operators like COUNT to be executed over their data. In this context, our methodology is based on historical queries and their answers to accurately predict ad-hoc queries’ answers. We focus on the widely used set-cardinality, i.e., COUNT, aggregation query, as COUNT is a fundamental operator for both internal data system optimizations and for aggregation-oriented data exploration and predictive analytics. We contribute a novel, query-driven Machine Learning (ML) model whose goals are to: (i) learn the query-answer space from past issued queries, (ii) associate the query space with local linear regression & associative function estimators, (iii) define query similarity, and (iv) predict the cardinality of the answer set of unseen incoming queries, referred to the Set Cardinality Prediction (SCP) problem. Our ML model incorporates incremental ML algorithms for ensuring high quality prediction results. The significance of contribution lies in that it (i) is the only query-driven solution applicable over general Big Data environments, which include restricted-access data, (ii) offers incremental learning adjusted for arriving ad-hoc queries, which is well suited for query-driven data exploration, and (iii) offers a performance (in terms of scalability, SCP accuracy, processing time, and memory requirements) that is superior to data-centric approaches. We provide a comprehensive performance evaluation of our model evaluating its sensitivity, scalability and efficiency for quality predictive analytics. In addition, we report on the development and incorporation of our ML model in Spark showing its superior performance compared to the Spark’s COUNT method

Q-learning with Nearest Neighbors

We consider model-free reinforcement learning for infinite-horizon discounted Markov Decision Processes (MDPs) with a continuous state space and unknown transition kernel, when only a single sample path under an arbitrary policy of the system is available. We consider the Nearest Neighbor Q-Learning (NNQL) algorithm to learn the optimal Q function using nearest neighbor regression method. As the main contribution, we provide tight finite sample analysis of the convergence rate. In particular, for MDPs with a $d$-dimensional state space and the discounted factor $\gamma \in (0,1)$, given an arbitrary sample path with "covering time" $L$, we establish that the algorithm is guaranteed to output an $\varepsilon$-accurate estimate of the optimal Q-function using $\tilde{O}\big(L/(\varepsilon^3(1-\gamma)^7)\big)$ samples. For instance, for a well-behaved MDP, the covering time of the sample path under the purely random policy scales as $\tilde{O}\big(1/\varepsilon^d\big),$ so the sample complexity scales as $\tilde{O}\big(1/\varepsilon^{d+3}\big).$ Indeed, we establish a lower bound that argues that the dependence of $\tilde{\Omega}\big(1/\varepsilon^{d+2}\big)$ is necessary.Comment: Accepted to NIPS 201

Doctor of Philosophy

dissertationWith the ever-increasing amount of available computing resources and sensing devices, a wide variety of high-dimensional datasets are being produced in numerous fields. The complexity and increasing popularity of these data have led to new challenges and opportunities in visualization. Since most display devices are limited to communication through two-dimensional (2D) images, many visualization methods rely on 2D projections to express high-dimensional information. Such a reduction of dimension leads to an explosion in the number of 2D representations required to visualize high-dimensional spaces, each giving a glimpse of the high-dimensional information. As a result, one of the most important challenges in visualizing high-dimensional datasets is the automatic filtration and summarization of the large exploration space consisting of all 2D projections. In this dissertation, a new type of algorithm is introduced to reduce the exploration space that identifies a small set of projections that capture the intrinsic structure of high-dimensional data. In addition, a general framework for summarizing the structure of quality measures in the space of all linear 2D projections is presented. However, identifying the representative or informative projections is only part of the challenge. Due to the high-dimensional nature of these datasets, obtaining insights and arriving at conclusions based solely on 2D representations are limited and prone to error. How to interpret the inaccuracies and resolve the ambiguity in the 2D projections is the other half of the puzzle. This dissertation introduces projection distortion error measures and interactive manipulation schemes that allow the understanding of high-dimensional structures via data manipulation in 2D projections