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Concept# Perceptron

Summary

In machine learning, the perceptron (or McCulloch-Pitts neuron) is an algorithm for supervised learning of binary classifiers. A binary classifier is a function which can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector.
History
History of artificial intelligence#Perceptrons and the attack on connectionism and AI winter#The abandonment of connectionism in 1969
The perceptron was invented in 1943 by Warren McCulloch and Walter Pitts. The first implementation was a machine built in 1958 at the Cornell Aeronautical Laboratory by Frank Rosenblatt, funded by the United States Office of Naval Research.
The perceptron was intended to be a machine, rather than a program, and while its first implementation was in software for the IBM 704, it was subse

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Proper initialization is one of the most important prerequisites for fast convergence of feed-forward neural networks like high order and multilayer perceptrons. This publication aims at determining the optimal variance (or range) for the initial weights and biases, which is the principal parameter of random initialization methods for both types of neural networks. An overview of random weight initialization methods for multilayer perceptrons is presented. These methods are extensively tested using eight real- world benchmark data sets and a broad range of initial weight variances by means of more than $30,000$ simulations, in the aim to find the best weight initialization method for multilayer perceptrons. For high order networks, a large number of experiments (more than $200,000$ simulations) was performed, using three weight distributions, three activation functions, several network orders, and the same eight data sets. The results of these experiments are compared to weight initialization techniques for multilayer perceptrons, which leads to the proposal of a suitable initialization method for high order perceptrons. The conclusions on the initialization methods for both types of networks are justified by sufficiently small confidence intervals of the mean convergence times.

Introduction: The unprecedented speed and scale of the COVID-19 pandemic necessitated the rapid implementation of untested public health measures to mitigate the consequences of viral spread. In the 8 months that have passed since the first recognized case, an enormous amount of research has been published evaluating the efficacy of the various policies implemented by different countries, however the majority of these studies focus on a specific region or time, over-representing high-income countries during periods of extreme transmission or “peak events”. The aim of this study is to provide a more general analysis that considers a global scope of the pandemic and the dynamic drivers that build effective policies to mitigate human interactions and slow the spread of disease. Methods: We collected a range of information regarding epidemic trends, weather, demographics, government response and mobility reports across the globe. We then built an hybrid Neural Network that combined an LSTM layer with a multilayer perceptron to infer the reproduction number from various non-epidemiological factors. The model was designed to predict the reproduction number (R-value) on 93 countries with available data and compare it to our ground truth estimate obtained from officially reported epidemiological data. Finally, we used an alternative model to assess the impact of public health measures on the epidemic. Findings: From the available features, we obtained the best performances using demographics combined with mobility features. The sanitary indices (beds/thousand, diabetes prevalence, ...) did not help the prediction and, more interestingly, the pressure indicator of historical weather forecast improved the prediction of the reproduction number by about 4.5%. This optimized model predicted the reproduction number with a mean absolute error of 0.254 across the 93 countries over the time of the epidemic. For many countries (Switzerland, United Kingdom, South Africa, ...) this error passed below 0.17. An alternative version of the model allowed us to estimate the impact of policies in terms of average reduction in reproduction number, and more importantly, allowed us to compare these trends between countries. For instance, we observe that the model showed that no policy had a positive impact in India as opposed to Switzerland, where most of them are associated to improved epidemic control. Conclusion: Understanding these complex interactions may allow individuals and policy makers to better adapt mitigation strategies to optimize the efficacy of the implemented policies.

2020Humans have the ability to learn. Having seen an object we can recognise it later. We can do this because our nervous system uses an efficient and robust visual processing and capabilities to learn from sensory input. On the other hand, designing algorithms to learn from visual data is a difficult task. More than fifty years ago, Rosenblatt proposed the perceptron algorithm. The perceptron learns from data examples a linear separation, which categorises the data in two classes. The algorithm served as a simple model of neuronal learning. Two further important ideas were added to the perceptron. First, to look for a maximal margin of separation. Second, to separate the data in a possibly high dimensional feature space, related nonlinearly to the initial space of the data, and allowing nonlinear separations. Important is that learning in the feature space can be performed implicitly and hence efficiently with the use of a kernel, a measure of similarity between two data points. The combination of these ideas led to the support vector machine, an efficient algorithm with high performance. In this thesis, we design an algorithm to learn the categorisation of data into multiple classes. This algorithm is applied to a real-time vision task, the recognition of human faces. Our algorithm can be seen as a generalisation of the support vector machine to multiple classes. It is shown how the algorithm can be efficiently implemented. To avoid a large number of small but time consuming updates of the variables limited accuracy computations are used. We prove a bound on the accuracy needed to find a solution. The proof motivates the use of a heuristic, which further increases efficiency. We derive a second implementation using a stochastic gradient descent method. This implementation is appealing as it has a direct interpretation and can be used in an online setting. Conceptually our approach differs from standard support vector approaches because examples can be rejected and are not necessarily attributed to one of the categories. This is natural in the context of a vision task. At any time, the sensory input can be something unseen before and hence cannot be recognised. Our visual data are images acquired with the recently developed adaptive vision sensor from CSEM. The vision sensor has two important features. First, like the human retina, it is locally adaptive to light intensity. Hence, the sensor has a high dynamic range. Second, the image gradient is computed on the sensor chip and is thus available directly from the sensor in real time. The sensor output is time encoded. The information about a strong local contrast is transmitted rst and the weakest contrast information at the end. To recognise faces, possibly moving in front of the camera, the sensor images have to be processed in a robust way. Representing images to exhibit local invariances is a common yet unsolved problem in computer vision. We develop the following representation of the sensor output. The image gradient information is decomposed into local histograms over contrast intensity. The histograms are local in position and direction of the gradient. Hence, the representation has local invariance properties to translation, rotation, and scaling. The histograms can be efficiently computed because the sensor output is already ordered with respect to the local contrast. Our support vector approach for multicategorical data uses the local histogram features to learn the recognition of faces. As recognition is time consuming, a face detection stage is used beforehand. We learn the detection features in an unsupervised manner using a specially designed optimisation procedure. The combined system to detect and recognise faces of a small group of individuals is efficient, robust, and reliable.