Aggregation Functions: A Guide for Practitioners by Gleb Beliakov

By Gleb Beliakov

A large creation to the subject of aggregation features is to be present in this e-book. It additionally presents a concise account of the houses and the most sessions of such features. a few state of the art concepts are awarded, besides many graphical illustrations and new interpolatory aggregation features. specific awareness is paid to identity and development of aggregation services from program particular specifications and empirical information.

Show description

Read or Download Aggregation Functions: A Guide for Practitioners PDF

Best intelligence & semantics books

Evolutionary Computation in Practice

This ebook is loaded with examples within which computing device scientists and engineers have used evolutionary computation - courses that mimic normal evolution - to unravel genuine difficulties. They aren t summary, mathematically extensive papers, yet debts of fixing vital difficulties, together with suggestions from the authors on the right way to stay away from universal pitfalls, maximize the effectiveness and potency of the hunt approach, and lots of different functional feedback.

Feedforward Neural Network Methodology (Springer Series in Statistics)

This decade has obvious an explosive development in computational pace and reminiscence and a quick enrichment in our figuring out of man-made neural networks. those components offer structures engineers and statisticians having the ability to construct versions of actual, monetary, and information-based time sequence and indications.

Artificial Intelligence for Humans, Volume 2: Nature-Inspired Algorithms

Nature could be a nice resource of concept for synthetic intelligence algorithms simply because its expertise is significantly extra complex than our personal. between its wonders are powerful AI, nanotechnology, and complicated robotics. Nature can for that reason function a consultant for real-life challenge fixing. during this publication, you are going to come upon algorithms stimulated by way of ants, bees, genomes, birds, and cells that supply sensible tools for plenty of different types of AI events.

Extra info for Aggregation Functions: A Guide for Practitioners

Sample text

58 (Lipschitz continuity). 6) where d(x, y) is a distance between x and y 15 . The smallest such number M is called the Lipschitz constant of f (in the distance d). Typically the distance is the Euclidean distance between vectors, d(x, y) = (x1 − y1 )2 + (x2 − y2 )2 + . . + (xn − yn )2 , but it can be chosen as any norm d(x, y) = ||x − y|| as a p-norm. A p-norm, p ≥ 1 is a function ||x||p = p, and ||x||∞ = max |xi |. ,n Thus, if the change in the input is δ = ||x−y||, then the output will change by at most M δ.

N ), input x we do not expect the output f (˜ x) to be substantially different from f (x). The Lipschitz constant M bounds the factor by which the noise is magnified. 59. Since f (0) = 0 and f (1) = 1, the Lipschitz √ constant of any aggregation function is M ≥ 1/||1||. For p-norms we have ||1|| = p n · 1 ≤ 1, that is M ≥ n−1/p , so in principle M can be smaller than 1. 60 (p-stable aggregation functions). Given p ≥ 1, an aggregation function is called p-stable if its Lipschitz constant in the p-norm || · ||p is 1.

We consider two simple techniques for constructing new aggregation functions. 5 Composition and transformation of aggregation functions 29 inputs and the second is based on iterative application of aggregation functions. Let us consider univariate strictly increasing bijections (hence continuous) ϕ1 , ϕ2 , . . , ϕn and ψ; ϕi , ψ : [0, 1] → [0, 1]. 82. Let ϕ1 , . . , ϕn , ψ : [0, 1] → [0, 1] be strictly increasing bijections. For any aggregation function f , the function g(x) = ψ(f (ϕ1 (x1 ), ϕ2 (x2 ), .

Download PDF sample

Rated 4.44 of 5 – based on 13 votes