Efficient Approximate Big Data Clustering: Distributed and Parallel Algorithms in the Spectrum of IoT Architectures

Clustering, the task of grouping together similar items, is a frequently used method for processing data, with numerous applications. Clustering the data generated by sensors in the Internet of Things, for instance, can be useful for monitoring and making control decisions. For example, a cyber physical environment can be monitored by one or more 3D laser-based sensors to detect the objects in that environment and avoid critical situations, e.g. collisions.With the advancements in IoT-based systems, the volume of data produced by, typically high-rate, sensors has become immense. For example, a 3D laser-based sensor with a spinning head can produce hundreds of thousands of points in each second. Clustering such a large volume of data using conventional clustering methods takes too long time, violating the time-sensitivity requirements of applications leveraging the outcome of the clustering. For example, collisions in a cyber physical environment must be prevented as fast as possible.The thesis contributes to efficient clustering methods for distributed and parallel computing architectures, representative of the processing environments in IoT- based systems. To that end, the thesis proposes MAD-C (abbreviating Multi-stage Approximate Distributed Cluster-Combining) and PARMA-CC (abbreviating Parallel Multiphase Approximate Cluster Combining). MAD-C is a method for distributed approximate data clustering. MAD-C employs an approximation-based data synopsis that drastically lowers the required communication bandwidth among the distributed nodes and achieves multiplicative savings in computation time, compared to a baseline that centrally gathers and clusters the data. PARMA-CC is a method for parallel approximate data clustering on multi-cores. Employing approximation-based data synopsis, PARMA-CC achieves scalability on multi-cores by increasing the synergy between the work-sharing procedure and data structures to facilitate highly parallel execution of threads. The thesis provides analytical and empirical evaluation for MAD-C and PARMA-CC

COMPACT REPRESENTATIONS OF UNCERTAINTY IN CLUSTERING

Flat clustering and hierarchical clustering are two fundamental tasks, often used to discover meaningful structures in data, such as subtypes of cancer, phylogenetic relationships, taxonomies of concepts, and cascades of particle decays in particle physics. When multiple clusterings of the data are possible, it is useful to represent uncertainty in clustering through various probabilistic quantities, such as the distribution over partitions or tree structures, and the marginal probabilities of subpartitions or subtrees. Many compact representations exist for structured prediction problems, enabling the efficient computation of probability distributions, e.g., a trellis structure and corresponding Forward-Backward algorithm for Markov models that model sequences. However, no such representation has been proposed for either flat or hierarchical clustering models. In this thesis, we present our work developing data structures and algorithms for computing probability distributions over flat and hierarchical clusterings, as well as for finding maximum a posteriori (MAP) flat and hierarchical clusterings, and various marginal probabilities, as given by a wide range of energy-based clustering models. First, we describe a trellis structure that compactly represents distributions over flat or hierarchical clusterings. We also describe related data structures that represent approximate distributions. We then present algorithms that, using these structures, allow us to compute the partition function, MAP clustering, and the marginal proba- bilities of a cluster (and sub-hierarchy, in the case of hierarchical clustering) exactly. We also show how these and related algorithms can be used to approximate these values, and analyze the time and space complexity of our proposed methods. We demonstrate the utility of our approaches using various synthetic data of interest as well as in two real world applications, namely particle physics at the Large Hadron Collider at CERN and in cancer genomics. We conclude with a brief discussion of future work

Spectral methods for multimodal data analysis

Spectral methods have proven themselves as an important and versatile tool in a wide range of problems in the fields of computer graphics, machine learning, pattern recognition, and computer vision, where many important problems boil down to constructing a Laplacian operator and finding a few of its eigenvalues and eigenfunctions. Classical examples include the computation of diffusion distances on manifolds in computer graphics, Laplacian eigenmaps, and spectral clustering in machine learning. In many cases, one has to deal with multiple data spaces simultaneously. For example, clustering multimedia data in machine learning applications involves various modalities or ``views'' (e.g., text and images), and finding correspondence between shapes in computer graphics problems is an operation performed between two or more modalities. In this thesis, we develop a generalization of spectral methods to deal with multiple data spaces and apply them to problems from the domains of computer graphics, machine learning, and image processing. Our main construction is based on simultaneous diagonalization of Laplacian operators. We present an efficient numerical technique for computing joint approximate eigenvectors of two or more Laplacians in challenging noisy scenarios, which also appears to be the first general non-smooth manifold optimization method. Finally, we use the relation between joint approximate diagonalizability and approximate commutativity of operators to define a structural similarity measure for images. We use this measure to perform structure-preserving color manipulations of a given image

Clustering in the Big Data Era: methods for efficient approximation, distribution, and parallelization

Data clustering is an unsupervised machine learning task whose objective is to group together similar items. As a versatile data mining tool, data clustering has numerous applications, such as object detection and localization using data from 3D laser-based sensors, finding popular routes using geolocation data, and finding similar patterns of electricity consumption using smart meters.The datasets in modern IoT-based applications are getting more and more challenging for conventional clustering schemes. Big Data is a term used to loosely describe hard-to-manage datasets. Particularly, large numbers of data points, high rates of data production, large numbers of dimensions, high skewness, and distributed data sources are aspects that challenge the classical data processing schemes, including clustering methods. This thesis contributes to efficient big data clustering for distributed and parallel computing architectures, representative of the processing environments in edge-cloud computing continuum. The thesis also proposes approximation techniques to cope with certain challenging aspects of big data.Regarding distributed clustering, the thesis proposes MAD-C, abbreviating Multi-stage Approximate Distributed Cluster-Combining. MAD-C leverages an approximation-based data synopsis that drastically lowers the required communication bandwidth among the distributed nodes and achieves multiplicative savings in computation time, compared to a baseline that centrally gathers and clusters the data. The thesis shows MAD-C can be used to detect and localize objects using data from distributed 3D laser-based sensors with high accuracy. Furthermore, the work in the thesis shows how to utilize MAD-C to efficiently detect the objects within a restricted area for geofencing purposes.Regarding parallel clustering, the thesis proposes a family of algorithms called PARMA-CC, abbreviating Parallel Multistage Approximate Cluster Combining. Using approximation-based data synopsis, PARMA-CC algorithms achieve scalability on multi-core systems by facilitating parallel execution of threads with limited dependencies which get resolved using fine-grained synchronization techniques. To further enhance the efficiency, PARMA-CC algorithms can be configured with respect to different data properties. Analytical and empirical evaluations show PARMA-CC algorithms achieve significantly higher scalability than the state-of-the-art methods while preserving a high accuracy.On parallel high dimensional clustering, the thesis proposes IP.LSH.DBSCAN, abbreviating Integrated Parallel Density-Based Clustering through Locality-Sensitive Hashing (LSH). IP.LSH.DBSCAN fuses the process of creating an LSH index into the process of data clustering, and it takes advantage of data parallelization and fine-grained synchronization. Analytical and empirical evaluations show IP.LSH.DBSCAN facilitates parallel density-based clustering of massive datasets using desired distance measures resulting in several orders of magnitude lower latency than state-of-the-art for high dimensional data.In essence, the thesis proposes methods and algorithmic implementations targeting the problem of big data clustering and applications using distributed and parallel processing. The proposed methods (available as open source software) are extensible and can be used in combination with other methods

Embed and Conquer: Scalable Embeddings for Kernel k-Means on MapReduce

The kernel $k$-means is an effective method for data clustering which extends the commonly-used $k$-means algorithm to work on a similarity matrix over complex data structures. The kernel $k$-means algorithm is however computationally very complex as it requires the complete data matrix to be calculated and stored. Further, the kernelized nature of the kernel $k$-means algorithm hinders the parallelization of its computations on modern infrastructures for distributed computing. In this paper, we are defining a family of kernel-based low-dimensional embeddings that allows for scaling kernel $k$-means on MapReduce via an efficient and unified parallelization strategy. Afterwards, we propose two methods for low-dimensional embedding that adhere to our definition of the embedding family. Exploiting the proposed parallelization strategy, we present two scalable MapReduce algorithms for kernel $k$-means. We demonstrate the effectiveness and efficiency of the proposed algorithms through an empirical evaluation on benchmark data sets.Comment: Appears in Proceedings of the SIAM International Conference on Data Mining (SDM), 201

SANNS: Scaling Up Secure Approximate k-Nearest Neighbors Search

The $k$-Nearest Neighbor Search ($k$-NNS) is the backbone of several cloud-based services such as recommender systems, face recognition, and database search on text and images. In these services, the client sends the query to the cloud server and receives the response in which case the query and response are revealed to the service provider. Such data disclosures are unacceptable in several scenarios due to the sensitivity of data and/or privacy laws. In this paper, we introduce SANNS, a system for secure $k$-NNS that keeps client's query and the search result confidential. SANNS comprises two protocols: an optimized linear scan and a protocol based on a novel sublinear time clustering-based algorithm. We prove the security of both protocols in the standard semi-honest model. The protocols are built upon several state-of-the-art cryptographic primitives such as lattice-based additively homomorphic encryption, distributed oblivious RAM, and garbled circuits. We provide several contributions to each of these primitives which are applicable to other secure computation tasks. Both of our protocols rely on a new circuit for the approximate top-$k$ selection from $n$ numbers that is built from $O(n + k^2)$ comparators. We have implemented our proposed system and performed extensive experimental results on four datasets in two different computation environments, demonstrating more than $18-31\times$ faster response time compared to optimally implemented protocols from the prior work. Moreover, SANNS is the first work that scales to the database of 10 million entries, pushing the limit by more than two orders of magnitude.Comment: 18 pages, to appear at USENIX Security Symposium 202

Exact Computation of a Manifold Metric, via Lipschitz Embeddings and Shortest Paths on a Graph

Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called the nearest neighbor metric. In fact, we prove the surprising result that a previously published $3$-approximation is an exact algorithm. The nearest neighbor metric can be viewed as a special case of a density-based distance used in machine learning, or it can be seen as an example of a manifold metric. Previous computational research on such metrics despaired of computing exact distances on account of the apparent difficulty of minimizing over all continuous paths between a pair of points. We leverage the exact computation of the nearest neighbor metric to compute sparse spanners and persistent homology. We also explore the behavior of the metric built from point sets drawn from an underlying distribution and consider the more general case of inputs that are finite collections of path-connected compact sets. The main results connect several classical theories such as the conformal change of Riemannian metrics, the theory of positive definite functions of Schoenberg, and screw function theory of Schoenberg and Von Neumann. We develop novel proof techniques based on the combination of screw functions and Lipschitz extensions that may be of independent interest.Comment: 15 page