Jingrui He's Analysis of Rare Categories PDF

By Jingrui He

ISBN-10: 3642228127

ISBN-13: 9783642228124

In many real-world difficulties, infrequent different types (minority periods) play crucial roles regardless of their severe shortage. the invention, characterization and prediction of infrequent different types of infrequent examples may perhaps defend us from fraudulent or malicious habit, relief medical discovery, or even store lives.

This publication makes a speciality of infrequent type research, the place the bulk sessions have delicate distributions, and the minority periods convey the compactness estate. in addition, it makes a speciality of the tough situations the place the help areas of the bulk and minority periods overlap. the writer has constructed potent algorithms with theoretical promises and stable empirical effects for the comparable concepts, and those are defined intimately. The ebook is appropriate for researchers within the sector of synthetic intelligence, specifically desktop studying and knowledge mining.

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9. On the Ecoli data set, to discover all the classes, MALICE needs 36 label requests, Interleave needs 41 label requests on average, RS needs 43 label requests on average, Kernel needs 78 label requests, and SEDER only needs 20 label requests; on the Glass data set, to discover all the classes, MALICE needs 18 label requests, Interleave needs 24 label requests on average, RS needs 31 label requests on average, Kernel needs 102 label requests, and SEDER needs 22 label requests. Therefore, on these ‘moderately’ skewed data sets, the performance of SEDER is better than or comparable with MALICE, which requires more prior information than SEDER including the number of classes in the data set and the proportions of different classes.

We refer to these three data sets as ‘highly’ skewed; and the remaining two (Ecoli and Glass) are referred to as ‘moderately’ skewed. 02 0 −6 −4 −2 0 2 4 6 (a) Underlying distribution of a one-dimensional synthetic data set: the majority class has a Gaussian distribution with a large variance; whereas the minority classes correspond to the two lower variance peaks. 200 180 160 140 120 100 80 60 40 20 0 −50 0 50 100 150 200 250 (b) Two-dimensional synthetic data set: there are 2000 examples from the majority class, denoted as blue dots; there are 267, 280, 84, and 150 examples from each minority class, denoted as red balls.

If 1. For minority class c, c = 2, . . , m, let Bc2 be the hyper-ball centered at bc with radius 2rc . , maxm c=2 min{ xi − xk |xi , xk ∈ S, xi − bc ≤ rc , xi − bc > 2rc } ≤ α. 2. , if xi , xk ∈ S, xi − bc ≤ rc , xk − bc ≤ rc , c, c = 2, . . , m, and c = c , then xi − xk > α. 3. , ∀x, y ∈ Rd , |f1 (x) − f1 (y)| ≤ β x−y , α where β ≤ minm c=2 ,rc ) p2c OV ( c2 2 . 2d+1 V (rc )2 r 4. , n ≥ max{maxm c=2 1 1 3m−3 3m−3 1 m m log , max log , max r 2 −d 2 2 4 2 c2 c=2 2(1−2 ) p c=2 p β 4 V ( δ δ 2κ p )4 c1 c 3m−3 δ }.

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Analysis of Rare Categories by Jingrui He

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