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Cluster Ensembles - A Knowledge Reuse Framework for Combining Multiple Partitions

by Alexander Strehl, Joydeep Ghosh, Claire Cardie - Journal of Machine Learning Research , 2002
"... This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse&ap ..."
Abstract - Cited by 603 (20 self) - Add to MetaCart
This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse

Multiplicative Partitions

by Marc Chamberland, Colin Johnson, Alice Nadeau, Bingxi Wu , 2009
"... New formulas for the multiplicative partition function are developed. Besides giving a fast algorithm for generating these partitions, new identities for additive partitions and the Riemann zeta function are also produced. ..."
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New formulas for the multiplicative partition function are developed. Besides giving a fast algorithm for generating these partitions, new identities for additive partitions and the Riemann zeta function are also produced.

I. MULTIPLE PARTITIONS

by Martin Smith
"... The Principle of Indifference was once regarded as a linchpin of probabilistic reasoning, but has now fallen into disrepute as a result of the so-called problem of multiple of partitions. In ‘Evidential symmetry and mushy credence ’ Roger White suggests that we have been too quick to jettison this p ..."
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The Principle of Indifference was once regarded as a linchpin of probabilistic reasoning, but has now fallen into disrepute as a result of the so-called problem of multiple of partitions. In ‘Evidential symmetry and mushy credence ’ Roger White suggests that we have been too quick to jettison

MULTIPLICATIVE PARTITIONS OF BIPARTITE NUMBERS

by Raymond N. Greenwell , 1989
"... For a positive integer n, let f(ri) be the number of multiplicative partitions of n. That is, f(n) represents the number of different factorizations of n, where two factorizations are considered the same if they differ only in the order of the factors. For example, /"(12) = 4, since 12 = 6*2 = ..."
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For a positive integer n, let f(ri) be the number of multiplicative partitions of n. That is, f(n) represents the number of different factorizations of n, where two factorizations are considered the same if they differ only in the order of the factors. For example, /"(12) = 4, since 12 = 6

On a Multiplicative Partition Function

by Yifan Yang , 2000
"... Let D(s) = P 1 m=1 amm s be the Dirichlet series generated by the innite product ..."
Abstract - Cited by 7 (1 self) - Add to MetaCart
Let D(s) = P 1 m=1 amm s be the Dirichlet series generated by the innite product

Muscle: multiple sequence alignment with high accuracy and high throughput

by Robert C. Edgar - NUCLEIC ACIDS RES , 2004
"... We describe MUSCLE, a new computer program for creating multiple alignments of protein sequences. Elements of the algorithm include fast distance estimation using kmer counting, progressive alignment using a new profile function we call the logexpectation score, and refinement using tree-dependent r ..."
Abstract - Cited by 2509 (7 self) - Add to MetaCart
We describe MUSCLE, a new computer program for creating multiple alignments of protein sequences. Elements of the algorithm include fast distance estimation using kmer counting, progressive alignment using a new profile function we call the logexpectation score, and refinement using tree

Multiple partitions, lattice paths and a . . .

by P. Jacob, P. Mathieu , 2006
"... A bijection is presented between (1): partitions with conditions fj + fj+1 ≤ k − 1 and f1 ≤ i − 1, where fj is the frequency of the part j in the partition, and (2): sets of k − 1 ordered partitions (n (1),n (2) , · · ·,n (k−1) ) such that n (j) ℓ ≥ n(j) ℓ+1 + 2j and n(j) mj ≥ j + max(j − i+1,0)+ ..."
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,0)+2j(mj+1+ · · ·+mk−1), where mj is the number of parts in n (j). This bijection entails an elementary and constructive proof of the Andrews multiple-sum enumerating partitions with frequency conditions. A very natural relation between the k − 1 ordered partitions and restricted paths is also

K.B.: Multi-Interval Discretization of Continuous-Valued Attributes for Classication Learning. In:

by Keki B Irani , Usama M Fayyad - IJCAI. , 1993
"... Abstract Since most real-world applications of classification learning involve continuous-valued attributes, properly addressing the discretization process is an important problem. This paper addresses the use of the entropy minimization heuristic for discretizing the range of a continuous-valued a ..."
Abstract - Cited by 832 (7 self) - Add to MetaCart
-valued attribute into multiple intervals. We briefly present theoretical evidence for the appropriateness of this heuristic for use in the binary discretization algorithm used in ID3, C4, CART, and other learning algorithms. The results serve to justify extending the algorithm to derive multiple intervals. We

Using GENERATINGFUNCTIONOLOGY to Enumerate Distinct-Multiplicity Partitions

by Doron Zeilberger
"... About a year ago, Herb Wilf[W1] posed, on-line, eight intriguing problems. I don’t know the answer to any of them, but I will say something about the sixth question. Herb Wilf’s 6th Question: Let T (n) be the set of partitions of n for which the (nonzero) multiplicities of its parts are all differen ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
About a year ago, Herb Wilf[W1] posed, on-line, eight intriguing problems. I don’t know the answer to any of them, but I will say something about the sixth question. Herb Wilf’s 6th Question: Let T (n) be the set of partitions of n for which the (nonzero) multiplicities of its parts are all

A NOTE ON MULTIPLICATIVE PARTITIONS OF BIPARTITE NUMBERS

by Sang Genu Hahn, Jun Kyo Kim , 1993
"... For a positive integer n, let f(n) be the number of essentially different ways of writing n as a product of factors greater than 1, where two factorizations of a positive integer are said to be essentially the same if they differ only in the order of the factors. For example, /(12) = 4, since 12 = ..."
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For a positive integer n, let f(n) be the number of essentially different ways of writing n as a product of factors greater than 1, where two factorizations of a positive integer are said to be essentially the same if they differ only in the order of the factors. For example, /(12) = 4, since 12 = 2-6-3-4 = 2-2-3. This function was introduced by Hughes and Shallit [1], who proved
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