In the data stream scenario, input arrives very rapidly and there is limited memory to store the input. Algorithms have to work with one or few passes over the data, space less than linear in the input size or time significantly less than the input size. In the past few years, a new theory has emerged for reasoning about algorithms that work within these constraints on space, time, and number of passes. Some of the methods rely on metric embeddings, pseudo-random computations, sparse approximation theory and communication complexity. The applications for this scenario include IP network traffic analysis, mining text message streams and processing massive data sets in general. Researchers in Theoretical Computer Science, Databases, IP Networking and Computer Systems are working on the data stream challenges. This article is an overview and survey of data stream algorithmics and is an updated version of [175].1

Abstract The k-means method is a widely used clustering technique that seeks to minimize the average squared distance between points in the same cluster. Although it offers no accuracy guarantees, its simplicity and speed are very appealing in practice. By augmenting k-means with a very simple, randomized seeding technique, we obtain an algorithm that is Θ(log k)-competitive with the optimal clustering. Preliminary experiments show that our augmentation improves both the speed and the accuracy of k-means, often quite dramatically.

Motivated by applications such as document and image classification in information retrieval, we consider the problem of clustering dynamic point sets in a metric space. We propose a model called incremental clustering which is based on a careful analysis of the requirements of the information retrieval application, and which should also be useful in other applications. The goal is to efficiently maintain clusters of small diameter as new points are inserted. We analyze several natural greedy algorithms and demonstrate that they perform poorly. We propose new deterministic and randomized incremental clustering algorithms which have a provably good performance. We complement our positive results with lower bounds on the performance of incremental algorithms. Finally, we consider the dual clustering problem where the clusters are of fixed diameter, and the goal is to minimize the number of clusters.

Traditional databases store sets of relatively static records with no pre-defined notion of time, unless timestamp attributes are explicitly added. While this model adequately represents commercial catalogues or repositories of personal information, many current and emerging applications require support for online analysis of rapidly changing data streams. Limitations of traditional DBMSs in supporting streaming applications have been recognized, prompting research to augment existing technologies and build new systems to manage streaming data. The purpose of this paper is to review recent work in data stream management systems, with an emphasis on application requirements, data models, continuous query languages, and query evaluation.

Abstract The recent advances in hardware and software have enabled the capture of different measurements of data in a wide range of fields. These measurements are generated continuously and in a very high fluctuating data rates. Examples include sensor networks, web logs, and computer network traffic. The storage, querying and mining of such data sets are highly computationally challenging tasks. Mining data streams is concerned with extracting knowledge structures represented in models and patterns in non stopping streams of information. The research in data stream mining has gained a high attraction due to the importance of its applications and the increasing generation of streaming information. Applications of data stream analysis can vary from critical scientific and astronomical applications to important business and financial ones. Algorithms, systems and frameworks that address streaming challenges have been developed over the past three years. In this review paper, we present the stateof-the-art in this growing vital field. 1-Introduction The intelligent data analysis has passed through a number of stages. Each stage addresses novel research issues that have arisen. Statistical exploratory data analysis represents the first stage. The goal was to explore the available data in order to test a specific hypothesis. With the advances in computing power, machine learning field has arisen. The objective was to find computationally efficient solutions to data analysis problems. Along with the progress in machine learning research, new data analysis problems have been addressed. Due to the increase in database sizes, new algorithms have been proposed to deal with the scalability issue. Moreover machine learning and statistical analysis techniques have been adopted and modified in order to address the problem of very large databases. Data mining is that interdisciplinary field of study that can extract models and patterns from large amounts of information stored in data repositories Recently, the data generation rates in some data sources become faster than ever before. This rapid generation of continuous streams of information has challenged our storage, computation and communication capabilities in computing systems. Systems, models and techniques have been proposed and developed over the past few years to address these challenges In this paper, we review the theoretical foundations of data stream analysis. Mining data stream systems, techniques are critically reviewed. Finally, we outline and discuss research problems in streaming mining field of study. These research issues should be addressed in order to realize robust systems that are capable of fulfilling the needs of data stream mining applications. The paper is organized as follows. Section 2 presents the theoretical background of data stream analysis. Mining data stream techniques and systems are reviewed in sections 3 and 4 respectively. Open and addressed research issues in this growing field are discussed in section 5. Finally section 6 summarizes this review paper. 2-Theoretical Foundations Research problems and challenges that have been arisen in mining data streams have its solutions using wellestablished statistical and computational approaches. We can categorize these solutions to data-based and task-based ones. In data-based solutions, the idea is to examine only a subset of the whole dataset or to transform the data vertically or horizontally to an approximate smaller size data representation. At the other hand, in task-based solutions, techniques from computational theory have been adopted to achieve time

The sliding window model is useful for discounting stale data in data stream applications. In this model, data elements arrive continually and only the most recent N elements are used when answering queries. We present a novel technique for solving two important and related problems in the sliding window model --- maintaining variance and maintaining a k-- median clustering. Our solution to the problem of maintaining variance provides a continually updated estimate of the variance of the last N values in a data stream with relative error of at most # using O( # 2 log N) memory. We present a constant-factor approximation algorithm which maintains an approximate k--median solution for the last N data points using O( N) memory, where # < 1/2 is a parameter which trades o# the space bound with the approximation factor of O(2 ).

Clustering is an important task in mining evolving data streams. Beside the limited memory and one-pass constraints, the nature of evolving data streams implies the following requirements for stream clustering: no assumption on the number of clusters, discovery of clusters with arbitrary shape and ability to handle outliers. While a lot of clustering algorithms for data streams have been proposed, they offer no solution to the combination of these requirements. In this paper, we present DenStream, a new approach for discovering clusters in an evolving data stream. The “dense ” micro-cluster (named core-micro-cluster) is introduced to summarize the clusters with arbitrary shape, while the potential core-micro-cluster and outlier micro-cluster structures are proposed to maintain and distinguish the potential clusters and outliers. A novel pruning strategy is designed based on these concepts, which guarantees the precision of the weights of the micro-clusters with limited memory. Our performance study over a number of real and synthetic data sets demonstrates the effectiveness and efficiency of our method.

In this paper, we show the existence of small coresets for the problems of computing k-median and k-means clustering for points in low dimension. In other words, we show that given a point set P in IR , one can compute a weighted set S P , of size log n), such that one can compute the k-median/means clustering on S instead of on P , and get an (1 + ")-approximation.

Abstract not found

Abstract not found