Possibility and Necessity Pattern Classification using an Interval Arithmetic Perceptron

Abstract

In the work presented in this paper, an Interval Arithmetic Perceptron (IAP) is used to detect the region in the input space to which an uncertainty decision should be appropriately associated. This region may be originated both by sub-regions which are not represented in the training set, and by subregions where the probabilities of the two classes are very similar. To train the IAP, an algorithm will be presented which in particular is able detect the two certainty regions and the uncertainty one. From the interval weights thus obtained, a confidence interval of the probability will also be evaluated. The algorithm has been used for studying a simple artificial problem and two real-world applications, the Iris and Breast Cancer databases. Regarding the latter application in particular, a statistical analysis of the results is presented, together with a discussion of the possible alternative classifications of the patterns attributed to the uncertainty region.

Parametric Functional Representation of Interval Number with Arithmetic Operations

“…Then the arithmetic sum of the two intervals S = A + B = [6,8] and the corresponding interval-valued functional form in parametric and symmetrical parametric from are given by s ( 1,3] and the interval-valued function in two different forms are specified by d (…”

“…Interval arithmetic operations [3,[6][7][8]12,29,30] studied by several researches in various approaches and form for investigation their problem with interval in real or complex domain. Interval arithmetic is an important and helpful tool in numerical analysis and modeling.…”

“…Let A =[4,5] and B =[2,3], then find the arithmetic operation using convex combination form of A + B, A − B, AB, A/B.Solution:The interval-valued function in convex combination form of A and B can be written as a ( p)= 5 p + 4 (1 − p) , b ( p) = 3 p + 2 (1 − p) .The addition A + B =[6,8] and the interval-valued function in convex combination form of the sum is s ( p) = 8 p + 6 (1 − p) .The subtraction A − B =[1,3] and convex combination form of the interval-valued function is d (p) = 5 p + 4 (1 − p) − {2 p + 3 (1 − p)} = 2 p + 1.The multiplication A × B =[8,15] and convex combination form of the interval-valued function for multiplication is m ( p) = (5 p + 4 (1 − p))(3 p …”

iMLP: Applying Multi-Layer Perceptrons to Interval-Valued Data

“…Drago and Ridella [21] propose a one-layer perceptron based on interval arithmetic with interval weights, where input data are classical (crisp) and output data are categorical. Their perceptron allows the detection of uncertainty regions in classification tasks.…”

A new approach to contextual learning using interval arithmetic and its applications for land-use classification

“…However, the reader can find very few works that employed IA to the context of machine learning applications. Drago and Ridella [4] , for instance, employed IA together with single Perceptron networks, and the very same group of authors validated Interval Arithmetic in the context Multilayer Perceptron neural networks (please, refer to the work conducted by Drago and Ridella [5] ). In this paper, we have shown how to achieve more accurate results in land-use classification by using features obtained through Interval Arithmetic concepts.…”