By Kenneth S. Miller

While the scholar of engineering or utilized technological know-how is first uncovered to stochastic strategies, or noise conception, he's often content material to control random variables officially as though they have been traditional capabilities. someday later the intense pupil turns into considering such difficulties because the validity of differentiating random variables and the translation of stochastic integrals, to claim not anything of the standard concerns linked to the interchange of the order of integration in a number of integrals. it truly is to this type of readers that this booklet is addressed. we try to investigate difficulties of the sort simply pointed out at an easy but rigorous point, and to adumbrate many of the actual purposes of the idea.

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48 G. SALTON TABLE 20 Average precision values at indicated recall points for three collections Standard term Phrases formed from Phrases formed from frequency high frequency medium frequency weights nondiscriminators discriminators /? 3854 SPT PT ST P Standard term frequency weighting (word stem run). Single terms, pairs and triples used in queries and documents. Pairs and triples used; corresponding single terms deleted. Single terms retained; triples added. Pairs added; corresponding singJe terms deleted.

Standard TF:f\ A. 0084 A :> B A ;> B 23 % 8% To summarize, several methods based on the multiplication of standard term frequency weights by inverse document frequency and discrimination values have been found that appear to offer high performance standards. Among the methods which offer statistically significant improvements over the standard term weighting procedures for all processing environments, the following are the most promising: (a) ft standard weights with elimination of poor discriminators; (b) /* • WFk without elimination, or with elimination of poor discriminators or of terms with high document frequency; (c) fkt-DVk with elimination of poor discriminators or of high frequency terms.

1, averaged over the 24 user queries that are utilized with each collection. TABLE 9 Comparison of binary and term frequency weighting with and without inverse document frequency normalization Binary Term frequency Binary with weights weights IDF weights with IDF $ /! 1 CRAN MED Time Term frequency A THEORY OF INDEXING 29 Four weighting procedures are used to produce the output of Table 9, including binary term weights £>,, term frequency weights /*, and binary as well as term frequency weights multiplied by an inverse document frequency factor, designated (IDF)k in Table 9.