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Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
process swap with the following properties: F pq (x) = 1(x) p = q F pq = Fq p F pr F pq , Fqr for all p, q, r S. The types of the distribution function and the triangle function are related to the model of uncertainty and the way of composition of the standard operations in the model. probabilistic neural network a term applied loosely to networks that exhibit some form of probabilistic behavior but also applied specifically to a type of network developed for pattern classification based upon statistical techniques for the estimation of probability densities. probability density function (PDF) (1) a function describing the relative probability of outcomes of an experiment. For experiments with discrete outcomes, the PDF is analogous to a relative frequency histogram. For experiments with continuous outcomes, the PDF is analogous to a relative frequency histogram where the category bin widths are reduced to zero. The total area underneath a PDF must always be unity. (2) the derivative of the cumulative distribution function (when the derivative exists). More formally, for a random x and any probabilistic event A, the probability density function px (x) satisfies Pr(x A) =
Application of Data-Driven Models in Drought Forecasting
Published in Saeid Eslamian, Faezeh Eslamian, Handbook of Drought and Water Scarcity, 2017
Shahab Araghinejad, Seyed-Mohammad Hosseini-Moghari, Saeid Eslamian
There are different types of artificial neural networks (ANNs). This chapter introduces the popular models of these networks including multilayer perceptron (MLP), radial basis function (RBF), generalized regression neural network (GRNN), and probabilistic neural network (PNN). Before further discussion, it is necessary to be familiar with some of the following definitions: Neuron: This is the basic unit of an ANN, which by using a transfer function and based on specific input variable determines a suitable response.Architecture: A network architecture includes a number of hidden layers, a number of neurons in each hidden layers, the specific transfer functions, the flow of data (straight or recurrent), and the way neurons are connected.Train network: Training is defined as the process of calibrating the network using pairs of input/output.
Deep convolutional neural networks accurately predict breast cancer using mammograms
Published in Waves in Random and Complex Media, 2023
Lal Hussain, Sara Ansari, Mamoona Shabir, Shahzad Ahmad Qureshi, Amjad Aldweesh, Abdulfattah Omar, Zahoor Iqbal, Syed Ahmed Chan Bukhari
The breast cancer diagnosis has accompanied classification and segmentation performance improvement due to the representation learning, a characteristic of DL, due to its auto-feature extraction proficiency as compared with the handpicked feature extraction requirement in ML [33]. The learning phase is characterized by the flow of information exhibiting the capability of self-leering [34]. In DL, the Bayesian framework determines uncertainty in the model output using a Bayesian neural network [35,36]. Donald F. Specht introduced a probabilistic neural network (PNN), using the Bayesian classification theory, consisting of three layers, viz. Input, Radial Basis, and Competitive layers [37,38]. PNN has been used to categorize mammography images into normal, benign, and malignant classes. The discrete wavelet transforms been used to find the input feature vector as handpicked features. They used seventy-five mammograms in their study and claimed an accuracy of 90%.
Heat treatment effects on tribological characteristics for AISI A8 tool steel and development of wear mechanism maps using K means clustering and neural networks
Published in Tribology - Materials, Surfaces & Interfaces, 2018
Nandakumar Pillai, Ram Karthikeyan, J. Paulo Davim
Probabilistic neural network (PNN) is a statistical algorithm used in classification problems. Here the operations are organised in a feed forward network with multiple layers of input, pattern, summation and output. PNN can be used for mapping, classification and to directly estimate posteriori probabilities. When an input is given, the hidden layer computes the distance between the input and training vector and produces the element close to the training vector. The summation layer computes the contribution of each class and generates net output as probability vectors [17]. A transfer function on output layer takes the maximum probabilities from the summation layer to give the final output. Nacereddine et al. [18] has used PNN in Computer-aided shape analysis and classification of weld defects in industrial radiography based invariant attributes. Neural network is used to predict and compare three body wear analysis of composite material by Rao et al. [19].
Novel Biometric Approach Based on Diaphragmatic Respiratory Movements Using Single-Lead EMG Signals
Published in IETE Journal of Research, 2023
Beyza Eraslan, Kutlucan Gorur, Feyzullah Temurtas
The probabilistic neural network (PNN) is a network based on the “probability density estimation”. PNN is fundamentally structured on Bayesian statistic approach and providing high training speed and remarkable correct recognition rates for signal classification problems [72]. This neural network has four layers namely the input layer, the pattern layer, the summation layer, and the output layer. The spread factor is important for the PNN model. Hence, an appropriate value depends on dataset [72]. In our study, the searching spread factor was made between (0.1–1) in 0.01 steps to ensure the optimal value and best performance of the PNN.