Concepts inTight results for clustering and summarizing data streams

Cluster analysis

Cluster analysis or clustering is the task of assigning a set of objects into groups (called clusters) so that the objects in the same cluster are more similar (in some sense or another) to each other than to those in other clusters. Clustering is a main task of explorative data mining, and a common technique for statistical data analysis used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, and bioinformatics.
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Data stream

In telecommunications and computing, a data stream is a sequence of digitally encoded coherent signals used to transmit or receive information that is in the process of being transmitted. In electronics and computer architecture, a data flow determines for which time which data item is scheduled to enter or leave which port of a systolic array, a Reconfigurable Data Path Array or similar pipe network, or other processing unit or block.
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Approximation algorithm

In computer science and operations research, approximation algorithms are algorithms used to find approximate solutions to optimization problems. Approximation algorithms are often associated with NP-hard problems; since it is unlikely that there can ever be efficient polynomial time exact algorithms solving NP-hard problems, one settles for polynomial time sub-optimal solutions.
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Upper and lower bounds

In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (P, ¿) is an element of P which is greater than or equal to every element of S. The term lower bound is defined dually as an element of P which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound.
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Histogram

In statistics, a histogram is a graphical representation showing a visual impression of the distribution of data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson. A histogram consists of tabular frequencies, shown as adjacent rectangles, erected over discrete intervals (bins), with an area equal to the frequency of the observations in the interval.
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APX

In complexity theory the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short). In simple terms, problems in this class have efficient algorithms that can find an answer within some fixed percentage of the optimal answer.
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Chernoff bound

In probability theory, the Chernoff bound, named after Herman Chernoff, gives exponentially decreasing bounds on tail distributions of sums of independent random variables. It is better than the first or second moment based tail bounds such as Markov's inequality or Chebyshev inequality, which only yield power-law bounds on tail decay. It is related to the (historically earliest) Bernstein inequalities, and to Hoeffding's inequality. Let X1, ...
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