This algorithm uses supervised learning methods for training Artificial Neural Networks. The whole idea of training multi-layer perceptrons is to compute the derivatives of the error function or gradient descent with respect to weights using the backpropagation algorithm. This algorithm is actually based on the linear algebraic operation with a goal of optimising error function by harnessing its intelligence and provisioning updates. In this post, we will focus on backpropagation and basic details around it on a high level in simple English. As mentioned above "Backpropagation" is an algorithm which uses supervised learning methods to compute the gradient descent (delta rule) with respect to weights.

Perceptron is a fundamental unit of the neural network which takes weighted inputs, process it and capable of performing binary classifications. In this post, we will discuss the working of the Perceptron Model. This is a follow-up blog post to my previous post on McCulloch-Pitts Neuron. In 1958 Frank Rosenblatt proposed the perceptron, a more generalized computational model than the McCulloch-Pitts Neuron. The important feature in the Rosenblatt proposed perceptron was the introduction of weights for the inputs.

As much as data science is playing a pivotal role everywhere, healthcare also finds it prominent application. Breast Cancer is the top rated type of cancer amongst women; which took away 627,000 lives alone. This high mortality rate due to breast cancer does need attention, for early detection so that prevention can be done in time. As a potential contributor to state-of-art technology development, data mining finds a multi-fold application in predicting Brest cancer. This work focuses on different classification techniques implementation for data mining in predicting malignant and benign breast cancer. Breast Cancer Wisconsin data set from the UCI repository has been used as experimental dataset while attribute clump thickness being used as an evaluation class. The performances of these twelve algorithms: Ada Boost M 1, Decision Table, J Rip, Lazy IBK, Logistics Regression, Multiclass Classifier, Multilayer Perceptron, Naive Bayes, Random forest and Random Tree are analyzed on this data set. Keywords- Data Mining, Classification Techniques, UCI repository, Breast Cancer, Classification Algorithms

Terrorism has become one of the most tedious problems to deal with and a prominent threat to mankind. To enhance counter-terrorism, several research works are developing efficient and precise systems, data mining is not an exception. Immense data is floating in our lives, though the scarce availability of authentic terrorist attack data in the public domain makes it complicated to fight terrorism. This manuscript focuses on data mining classification techniques and discusses the role of United Nations in counter-terrorism. It analyzes the performance of classifiers such as Lazy Tree, Multilayer Perceptron, Multiclass and Na\"ive Bayes classifiers for observing the trends for terrorist attacks around the world. The database for experiment purpose is created from different public and open access sources for years 1970-2015 comprising of 156,772 reported attacks causing massive losses of lives and property. This work enumerates the losses occurred, trends in attack frequency and places more prone to it, by considering the attack responsibilities taken as evaluation class.

A human brain is capable of continual learning by nature; however the current mainstream deep neural networks suffer from a phenomenon named catastrophic forgetting (i.e., learning a new set of patterns suddenly and completely would result in fully forgetting what has already been learned). In this paper we propose a generic learning model, which regards a learning system as a fiber bundle. By comparing the learning performance of our model with conventional ones whose neural networks are multilayer perceptrons through a variety of machine-learning experiments, we found our proposed model not only enjoys a distinguished capability of continual learning but also bears a high information capacity. In addition, we found in some learning scenarios the learning performance can be further enhanced by making the learning time-aware to mimic the episodic memory in human brain. Last but not least, we found that the properties of forgetting in our model correspond well to those of human memory. This work may shed light on how a human brain learns.

Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or the solution space that they attempt to approximate. This is mainly because of their homogenous configuration based solely on the linear neuron model. Therefore, while they learn very well those problems with a monotonous, relatively simple and linearly separable solution space, they may entirely fail to do so when the solution space is highly nonlinear and complex. Sharing the same linear neuron model with two additional constraints (local connections and weight sharing), this is also true for the conventional Convolutional Neural Networks (CNNs) and, it is, therefore, not surprising that in many challenging problems only the deep CNNs with a massive complexity and depth can achieve the required diversity and the learning performance. In order to address this drawback and also to accomplish a more generalized model over the convolutional neurons, this study proposes a novel network model, called Operational Neural Networks (ONNs), which can be heterogeneous and encapsulate neurons with any set of operators to boost diversity and to learn highly complex and multi-modal functions or spaces with minimal network complexity and training data. Finally, a novel training method is formulated to back-propagate the error through the operational layers of ONNs. Experimental results over highly challenging problems demonstrate the superior learning capabilities of ONNs even with few neurons and hidden layers.

Not so long ago I published the simplest perceptron you'll ever see, code I wrote after a machine learning class, a while back. Ever since that I've been meaning to do something cool with it. So, browsing some more old codes I found a little game I made when I was studing fake 3D perspective, so I thought: can my perceptron play this game? So I gave the game code a little brushing, wrote some more code to capture the data of me playing it (I played until I got a score of 33 points) and feed it to my neural net. After that I just played with the learning rate and iterations and let it play the game on it's own.

We study the problem of efficient online multiclass linear classification with bandit feedback, where all examples belong to one of $K$ classes and lie in the $d$-dimensional Euclidean space. Previous works have left open the challenge of designing efficient algorithms with finite mistake bounds when the data is linearly separable by a margin $\gamma$. In this work, we take a first step towards this problem. We consider two notions of linear separability, \emph{strong} and \emph{weak}. 1. Under the strong linear separability condition, we design an efficient algorithm that achieves a near-optimal mistake bound of $O\left( K/\gamma^2 \right)$. 2. Under the more challenging weak linear separability condition, we design an efficient algorithm with a mistake bound of $\min (2^{\widetilde{O}(K \log^2 (1/\gamma))}, 2^{\widetilde{O}(\sqrt{1/\gamma} \log K)})$. Our algorithm is based on kernel Perceptron, which is inspired by the work of \citet{Klivans-Servedio-2008} on improperly learning intersection of halfspaces.

Like most learning algorithms, the multilayer perceptrons (MLP) is designed to learn a vector of parameters from data. However, in certain scenarios we are interested in learning structured parameters (predictions) in the form of symmetric positive definite matrices. Here, we introduce a variant of the MLP, referred to as the matrix MLP, that is specialized at learning symmetric positive definite matrices. We also present an application of the model within the context of the variational autoencoder (VAE). Our formulation of the VAE extends the vanilla formulation to the cases where the recognition and the generative networks can be from the parametric family of distributions with dense covariance matrices. Two specific examples are discussed in more detail: the dense covariance Gaussian and its generalization, the power exponential distribution. Our new developments are illustrated using both synthetic and real data.

In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and expensive high-fidelity model are available. The method relies on proper orthogonal decomposition (POD) to generate the high-fidelity reduced basis and a shallow multilayer perceptron to learn the high-fidelity reduced coefficients. In contrast to other methods, one distinct feature of the proposed method is to incorporate the features extracted from the low-fidelity data as the input feature, this approach not only improves the predictive capability of the neural network but also enables the decoupling the high-fidelity simulation from the online stage. Due to its nonin-trusive nature, it is applicable to general parameterized problems. We also provide several numerical examples to illustrate the effectiveness and performance of the proposed method.