Solving k-center Clustering (with Outliers) in MapReduce and Streaming, almost as Accurately as Sequentially.

Center-based clustering is a fundamental primitive for data analysis and becomes very challenging for large datasets. In this paper, we focus on the popular k-center variant which, given a set S of points from some metric space and a parameter k0, the algorithms yield solutions whose approximation ratios are a mere additive term \u3f5 away from those achievable by the best known polynomial-time sequential algorithms, a result that substantially improves upon the state of the art. Our algorithms are rather simple and adapt to the intrinsic complexity of the dataset, captured by the doubling dimension D of the metric space. Specifically, our analysis shows that the algorithms become very space-efficient for the important case of small (constant) D. These theoretical results are complemented with a set of experiments on real-world and synthetic datasets of up to over a billion points, which show that our algorithms yield better quality solutions over the state of the art while featuring excellent scalability, and that they also lend themselves to sequential implementations much faster than existing ones

Greedy Strategy Works for k-Center Clustering with Outliers and Coreset Construction

We study the problem of k-center clustering with outliers in arbitrary metrics and Euclidean space. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithm with low complexity for this problem. Our idea is inspired by the greedy method, Gonzalez\u27s algorithm, for solving the problem of ordinary k-center clustering. Based on some novel observations, we show that this greedy strategy actually can handle k-center clustering with outliers efficiently, in terms of clustering quality and time complexity. We further show that the greedy approach yields small coreset for the problem in doubling metrics, so as to reduce the time complexity significantly. Our algorithms are easy to implement in practice. We test our method on both synthetic and real datasets. The experimental results suggest that our algorithms can achieve near optimal solutions and yield lower running times comparing with existing methods

Advances in Big Data Analytics: Algorithmic Stability and Data Cleansing

Analysis of what has come to be called “big data” presents a number of challenges as data continues to grow in size, complexity and heterogeneity. To help addresses these challenges, we study a pair of foundational issues in algorithmic stability (robustness and tuning), with application to clustering in high-throughput computational biology, and an issue in data cleansing (outlier detection), with application to pre-processing in streaming meteorological measurement. These issues highlight major ongoing research aspects of modern big data analytics. First, a new metric, robustness, is proposed in the setting of biological data clustering to measure an algorithm’s tendency to maintain output coherence over a range of parameter settings. It is well known that different algorithms tend to produce different clusters, and that the choice of algorithm is often driven by factors such as data size and type, similarity measure(s) employed, and the sort of clusters desired. Even within the context of a single algorithm, clusters often vary drastically depending on parameter settings. Empirical comparisons performed over a variety of algorithms and settings show highly differential performance on transcriptomic data and demonstrate that many popular methods actually perform poorly. Second, tuning strategies are studied for maximizing biological fidelity when using the well-known paraclique algorithm. Three initialization strategies are compared, using ontological enrichment as a proxy for cluster quality. Although extant paraclique codes begin by simply employing the first maximum clique found, results indicate that by generating all maximum cliques and then choosing one of highest average edge weight, one can produce a small but statistically significant expected improvement in overall cluster quality. Third, a novel outlier detection method is described that helps cleanse data by combining Pearson correlation coefficients, K-means clustering, and Singular Spectrum Analysis in a coherent framework that detects instrument failures and extreme weather events in Atmospheric Radiation Measurement sensor data. The framework is tested and found to produce more accurate results than do traditional approaches that rely on a hand-annotated database

Distributed k-Means with Outliers in General Metrics

Center-based clustering is a pivotal primitive for unsupervised learning and data analysis. A popular variant is the k-means problem, which, given a set P of points from a metric space and a parameter k < |P|, requires finding a subset S ⊂ P of k points, dubbed centers, which minimizes the sum of all squared distances of points in P from their closest center. A more general formulation, introduced to deal with noisy datasets, features a further parameter z and allows up to z points of P (outliers) to be disregarded when computing the aforementioned sum. We present a distributed coreset-based 3-round approximation algorithm for k-means with z outliers for general metric spaces, using MapReduce as a computational model. Our distributed algorithm requires sublinear local memory per reducer, and yields a solution whose approximation ratio is an additive term O(γ) away from the one achievable by the best known polynomial-time sequential (possibly bicriteria) approximation algorithm, where γ can be made arbitrarily small. An important feature of our algorithm is that it obliviously adapts to the intrinsic complexity of the dataset, captured by its doubling dimension D. To the best of our knowledge, no previous distributed approaches were able to attain similar quality-performance tradeoffs for general metrics

Parallelization of Partitioning Around Medoids (PAM) in K-Medoids Clustering on GPU

K-medoids clustering is categorized as partitional clustering. K-medoids offers better result when dealing with outliers and arbitrary distance metric also in the situation when the mean or median does not exist within data. However, k-medoids suffers a high computational complexity. Partitioning Around Medoids (PAM) has been developed to improve k-medoids clustering, consists of build and swap steps and uses the entire dataset to find the best potential medoids. Thus, PAM produces better medoids than other algorithms. This research proposes the parallelization of PAM in k-medoids clustering on GPU to reduce computational time at the swap step of PAM. The parallelization scheme utilizes shared memory, reduction algorithm, and optimization of the thread block configuration to maximize the occupancy. Based on the experiment result, the proposed parallelized PAM k-medoids is faster than CPU and Matlab implementation and efficient for large dataset

Outlier Detection In Big Data

The dissertation focuses on scaling outlier detection to work both on huge static as well as on dynamic streaming datasets. Outliers are patterns in the data that do not conform to the expected behavior. Outlier detection techniques are broadly applied in applications ranging from credit fraud prevention, network intrusion detection to stock investment tactical planning. For such mission critical applications, a timely response often is of paramount importance. Yet the processing of outlier detection requests is of high algorithmic complexity and resource consuming. In this dissertation we investigate the challenges of detecting outliers in big data -- in particular caused by the high velocity of streaming data, the big volume of static data and the large cardinality of the input parameter space for tuning outlier mining algorithms. Effective optimization techniques are proposed to assure the responsiveness of outlier detection in big data. In this dissertation we first propose a novel optimization framework called LEAP to continuously detect outliers over data streams. The continuous discovery of outliers is critical for a large range of online applications that monitor high volume continuously evolving streaming data. LEAP encompasses two general optimization principles that utilize the rarity of the outliers and the temporal priority relationships among stream data points. Leveraging these two principles LEAP not only is able to continuously deliver outliers with respect to a set of popular outlier models, but also provides near real-time support for processing powerful outlier analytics workloads composed of large numbers of outlier mining requests with various parameter settings. Second, we develop a distributed approach to efficiently detect outliers over massive-scale static data sets. In this big data era, as the volume of the data advances to new levels, the power of distributed compute clusters must be employed to detect outliers in a short turnaround time. In this research, our approach optimizes key factors determining the efficiency of distributed data analytics, namely, communication costs and load balancing. In particular we prove the traditional frequency-based load balancing assumption is not effective. We thus design a novel cost-driven data partitioning strategy that achieves load balancing. Furthermore, we abandon the traditional one detection algorithm for all compute nodes approach and instead propose a novel multi-tactic methodology which adaptively selects the most appropriate algorithm for each node based on the characteristics of the data partition assigned to it. Third, traditional outlier detection systems process each individual outlier detection request instantiated with a particular parameter setting one at a time. This is not only prohibitively time-consuming for large datasets, but also tedious for analysts as they explore the data to hone in on the most appropriate parameter setting or on the desired results. We thus design an interactive outlier exploration paradigm that is not only able to answer traditional outlier detection requests in near real-time, but also offers innovative outlier analytics tools to assist analysts to quickly extract, interpret and understand the outliers of interest. Our experimental studies including performance evaluation and user studies conducted on real world datasets including stock, sensor, moving object, and Geolocation datasets confirm both the effectiveness and efficiency of the proposed approaches