P. Diaconis. Group Representation in Probability and Statistics. IMS Lecture Series 11, IMS, 1988. Home/Search Document Not in Database Summary Related Articles Check |
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Approximate Counting of Inversions in a Data Stream - Ajtai, Jayram, Kumar.. (2002) (6 citations) (Correct)
....the number of inversions between two lists in O(ffl Gamma3 p n log n(log n log m) space. 10 6 Discussion In the context of measuring the sortedness of data, there are several natural ways to do so: there is a list of at least six well known metrics on the permutation group S n (cf. [6]) and each one of them may be relevant to some sorting algorithm. However, some of them are quite inappropriate for practice; for example, computing the minimum number of reversals needed to sort an array is NP hard [5] the case of transpositions is still open) Some of the more tractable ....
P. Diaconis. Group Representation in Probability and Statistics. IMS Lecture Series 11, IMS, 1988.
Rank Aggregation Methods for the Web - Dwork, Kumar, Naor, Sivakumar (2001) (36 citations) (Correct)
....jT ) will be a new list that contains only elements from T . Notice that if happens to contain all the elements in T , then jT is a full list with respect to T . 2.1. 1 Distance measures Howdowe measure distance between two full lists with respect to a set S Two popular distance measures are [12]: 1) The Spearman footrule distance is the sum, over all elements i 2 S, of the absolute difference between the rank of i according to the two lists. Formally, given two full lists oe and , the distance is given by F (oe#) P jSj i=1 joe(i) i)j. After dividing this number by the maximum ....
....large extent, our interpretations of experimental results will be in terms of these distance measures. While these distance measures seem natural, why these measures are good is moot. We do not delve into such discussions here# the interested reader can find such arguments in the books by Diaconis [12], Critchlow [11] or Marden [17] 2.1.2 Optimal rank aggregation In the generic context of rank aggregation, the notion of better depends on what distance measure we strivetooptimize. Suppose we wish to optimize Kendall distance, the question then is: given (full or partial) lists 1#: # k ....
P. Diaconis. Group Representation in Probability and Statistics. IMS Lecture Series 11, IMS, 1988.
Approximate Counting of Inversions in a Data Stream - Ajtai, Jayram, Kumar.. (2002) (6 citations) (Correct)
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P. Diaconis. Group Representation in Probability and Statistics. IMS Lecture Series 11, IMS, 1988.
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