Structural Risk Minimization Principle Based on Complex Fuzzy Random Samples
نویسندگان
چکیده
Statistical Learning Theory is commonly regarded as a sound framework within which we handle a variety of learning problems in presence of small size data samples. It has become a rapidly progressing research area in machine learning. The theory is based on real random samples and as such is not ready to deal with the statistical learning problems involving complex fuzzy random samples, which we may encounter in real world scenarios. This paper explores statistical learning theory based on complex fuzzy random samples. Firstly, the definition of complex fuzzy random variable is introduced. Next the concepts and some properties of the mathematical expectation and independence of complex fuzzy random variables are provided. Secondly, the concepts of annealed entropy, growth function and VC dimension of measurable complex fuzzy set valued functions are proposed, and the bounds on the rate of uniform convergence of learning process based on complex fuzzy random samples are constructed. Thirdly, on the basis of these bounds, the idea of the complex fuzzy structural risk minimization principle is presented. Finally, the consistency of this principle is proven and the bound on the asymptotic rate of convergence is derived.
منابع مشابه
An Epsilon Hierarchical Fuzzy Twin Support Vector Regression
—The research presents -hierarchical fuzzy twin support vector regression (-HFTSVR) based on -fuzzy twin support vector regression (-FTSVR) and -twin support vector regression (-TSVR). -FTSVR is achieved by incorporating trapezoidal fuzzy numbers to -TSVR which takes care of uncertainty existing in forecasting problems. -FTSVR determines a pair of -insensitive proximal functions by so...
متن کاملBoosted ARTMAP: Modifications to fuzzy ARTMAP motivated by boosting theory
In this paper, several modifications to the Fuzzy ARTMAP neural network architecture are proposed for conducting classification in complex, possibly noisy, environments. The goal of these modifications is to improve upon the generalization performance of Fuzzy ART-based neural networks, such as Fuzzy ARTMAP, in these situations. One of the major difficulties of employing Fuzzy ARTMAP on such le...
متن کاملCluster-Based Image Segmentation Using Fuzzy Markov Random Field
Image segmentation is an important task in image processing and computer vision which attract many researchers attention. There are a couple of information sets pixels in an image: statistical and structural information which refer to the feature value of pixel data and local correlation of pixel data, respectively. Markov random field (MRF) is a tool for modeling statistical and structural inf...
متن کاملLearning from Imprecise and Fuzzy Observations: Data Disambiguation through Generalized Loss Minimization
Methods for analyzing or learning from “fuzzy data” have attracted increasing attention in recent years. In many cases, however, existing methods (for precise, non-fuzzy data) are extended to the fuzzy case in an ad-hoc manner, and without carefully considering the interpretation of a fuzzy set when being used for modeling data. Distinguishing between an ontic and an epistemic interpretation of...
متن کاملStructural risk minimization for reduced-bias time-frequency-based detectors design
Detectors design requires substantial knowledge of the observation statistical properties, conditionally to the competing hypotheses H0 and H1. However, many applications involve complex phenomena, in which few a priori information is available. Several methods of designing time-frequency-based (TF) receivers from labeled training data have been proposed. Unfortunately, the resulting detectors ...
متن کامل