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Quantum Preprocessing for Deep Convolutional Neural Networks in Atherosclerosis Detection
Published in Siddhartha Bhattacharyya, Mario Köppen, Elizabeth Behrman, Ivan Cruz-Aceves, Hybrid Quantum Metaheuristics, 2022
Siddhartha Bhattacharyya, Mario Köppen, Elizabeth Behrman, Ivan Cruz-Aceves
Lastly, the SoftMax function converts a real input vector into a vector of probabilities. Therefore, the elements of the output vector must sum up to 1. The SoftMax function applied on the vector x is computed as SoftMax(x)=ex∑i=1Nexi.
Neural Network
Published in Ravishankar Chityala, Sridevi Pudipeddi, Image Processing and Acquisition using Python, 2020
Ravishankar Chityala, Sridevi Pudipeddi
The model is built by passing 3 Dense layers to the Sequential class. The first layer has 64 nodes, the second layer has 64 nodes. The first 2 layers use the Rectified Linear Unit (RELU) activation function for non-linearity. The last layer produces a vector of length 10. This vector is passed through a softmax function (Equation 11.16). The output of a softmax function is a probability distribution as each of the values corresponds to the probability of a given digit and also the sum of all the values in the vector equates to 1. Once we obtain this vector, determining the corresponding digit can be accomplished by finding the position in the vector with the highest probability value. si=exi∑iexi
Thinking Deeply: Neural Networks and Deep Learning
Published in Jesús Rogel-Salazar, Advanced Data Science and Analytics with Python, 2020
It may be the case that in our application we are interested in generating probabilities as the outcomes of the activation layer. In this case, we can make use of the softmax activation function. This function is effectively a generalisation of the sigmoid function. It takes real values as input and maps them to a probability distribution where entry is in the range (0, 1]. Furthermore, all the entries add up to 1. The softmax activation function is given by Equation C.1 and a plot can be seen in Figure 4.6. ()softmax(xi)=σ(zi)=exp(xi)∑j=1Nexp(xj),fori=1,…,k.As the entries of a softmax function add up to 1, it can be used to draw probabilities.
A study on relationship between prediction uncertainty and robustness to noisy data
Published in International Journal of Systems Science, 2023
Hufsa Khan, Xizhao Wang, Han Liu
The softmax function takes as input a vector z of K real numbers, and normalises it into a probability distribution involving probabilities proportional to the exponential of the input numbers. Suppose we have a -dimensional input vector, i.e. = ( ), , and where , it can be transformed into a -dimensional probability vector, such as = (). The standard softmax function is defined as follows: where and 0 is a temperature parameter which has a great effect on the classification performance. In this study, we will investigate the sensitivity analysis of this important parameter (i.e. τ) in the context of model robustness and classification accuracy.
Intelligent painting identification based on image perception in multimedia enterprise
Published in Enterprise Information Systems, 2022
Yunzhong Wang, Ziying Xu, Siyue Bai, Qiyuan Wang, Ying Chen, Weifeng Li, Xiaoling Huang, Yun Ge
Lastly, we explained the distinctions between softmax classification and Modified IBS classification briefly. Usually, the softmax function is applied at the end of neural network as the output layer for traditional multi-classification (Mosteller and Wallace 1984). It maps multiple scalars into a probability distribution ranged from 0 to 1, with the sum of all outputs is 1. The outputs of the softmax function are a distribution of probability over different possible outcomes. In fact, it is the gradient-log-normaliser of the categorical probability distribution. How does the softmax function work out for classification? The category corresponding to the maximum probability value in the distribution is the classified result. Unlikely, the Modified IBS method provided a distance between two images instead of a probability. For two paintings of the same style, the IBS distance between them is smaller than that of two different styles. Such an approach allows us to capture the degree of similarity of two images and classify them into their specific categories. Yet the outputs of softmax can only predict the classification.
Research on fault diagnosis of time-domain vibration signal based on convolutional neural networks
Published in Systems Science & Control Engineering, 2019
Mingyong Li, Qingmin Wei, Hongya Wang, Xuekang Zhang
The fully connected (FC) layer classifies the features extracted from the convolution layer. Specifically, the output of the last pooling layer is firstly developed into a one-dimensional feature vector as the input of the FC layer. Then the input and output are fully connected. The activation function used by the hidden layer is ReLU, and the activation function used by the output layer is Softmax. The purpose of Softmax function is to convert the input neurons into the probability distribution with a sum of 1, which is conducive to the establishment of the subsequent multi-classification objective function. The forward propagation formula of the FC layer is shown as follows: where is the weight between the i-th neuron in layer l and the j-th neuron in layer l + 1. is the logits value of the j-th output neuron in layer l + 1. is the offset value of all neurons in the layer l to the j-th neuron in layer l + 1.