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## Estimating dominance norms of multiple data streams (2003)

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### Other Repositories/Bibliography

Venue: | in Proceedings of the 11th European Symposium on Algorithms (ESA |

Citations: | 29 - 8 self |

### Citations

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(Show Context)
Citation Context ...ults in data streams has focused on using various Lp norms for individualdistributionsto compare and collate informationfrom different data streams, for example, ( � i (�j ai,j) p ) 1/p for 0 < p ≤ 2 =-=[1, 11, 17]-=- and related notions such as Hamming norms � i ((�j ai,j) �= 0) [4]. While these norms are suitable for capturing comparative trends in multiple data streams, they are not applicable for computing the... |

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A method for simulating stable random variables.
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Citation Context ...table distributions for general α, it is possible to draw values from such distributions for arbitrary α by using a transform from two independent uniform random variables. Lemma 3 (Equation (2.3) of =-=[3]-=-). Let U be a uniform random variable on [0, 1] and Θ ]. Then uniform on [ −π 2 , π 2 S(α, 0) ∼ sin αΘ (cos Θ) 1/α � cos(1 − α)Θ − ln U � 1−α α We also make use of two other results on random variable... |

235 | Pseudorandom Generator for Space Bounded Computation - Nisan - 1990 |

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191 | Counting distinct elements in a data stream
- Bar-Yossef, Jayram, et al.
- 2002
(Show Context)
Citation Context ... log M) log 1 δ ) space, and amortized time ) per item (here Õ surpresses log log n and log 1 ɛ factors). Õ( 1 ɛ log2 M log log M δɛ D 4 3 2 0 jsThis follows by adopting the third method described in =-=[2]-=-, which is the most space efficient method for finding the number of distinct elements in a stream that is in the literature. The space required for each D is O(( 1 ɛ2 + log M) log 1 1 ɛ log log(M) lo... |

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51 | Estimating rarity and similarity over data stream windows.
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(Show Context)
Citation Context ...ches which are used in ensemble as indicators when observing data streams include monitoring those items that occur very frequently (the “heavy hitters” of [12, 10]), and those that occur very rarely =-=[8]-=-. We mention only work related to our current interest in computing dominance norms of streams. For a more general overview of issues and algorithms in processing data streams, see the survey [19]. 2 ... |

35 | Oceanic and Atmospheric Administration), - NOAA - 2011 |

20 |
Comparing data streams using hamming norms
- Cormode, Datar, et al.
- 2002
(Show Context)
Citation Context ...stributionsto compare and collate informationfrom different data streams, for example, ( � i (�j ai,j) p ) 1/p for 0 < p ≤ 2 [1, 11, 17] and related notions such as Hamming norms � i ((�j ai,j) �= 0) =-=[4]-=-. While these norms are suitable for capturing comparative trends in multiple data streams, they are not applicable for computing the various dominance norms (max, min, count or relative). Most relate... |

16 | Extensions of Lipshitz mapping into Hilbert space. Contemporary Mathematics - Johnson, Lindenstrauss - 1984 |

11 |
A note on the behaviour of the stable distributions for small index α. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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(Show Context)
Citation Context ...||a|| α α ≤ (1 + ɛ) dommax(a) lim α→0 + median(|cX| α ) = |c| α median(|X| α ) = |c|α ln 2 Proof: Let E be distributed with the exponential distribution with mean one. Then limα→0 + |S(α, β)| α = E−1 =-=[7]-=-. The density of E−1 is f(x) = x−2 exp(−1/x), x > 0 and the cumulative density is F (x) = � x 0 f(x)dx = exp(−1/x) so in the limit, median(E −1 ) = F −1 (1/2) = 1/ ln 2 ⊓⊔ Consequently ∀k.|zk| α ∼ ||a... |

7 | Fast mining of tabular data via approximate distance computations
- Cormode, Indyk, et al.
- 2002
(Show Context)
Citation Context ...stable distributions to improve the space requirements. 3.1 Stable Distributions Indyk pioneered the use of Stable Distributions in data streams and since then have received a great deal of attention =-=[17, 5, 4, 16]-=-. Throughout our discussion of distributions, we shall use ∼ for the equivalence relation meaning “is equivalent in distribution to”. A stable distribution is defined by four parameters. These are (i)... |

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2 | An approximate L 1 -dierence algorithm for massive data streams - Feigenbaum, Kannan, et al. - 1999 |