The document is a report on implementing and testing a radial basis function neural network for clustering iris flower data. It introduces RBF networks and the methodology used, which involved locating RBF nodes as cluster centers, calculating Gaussian functions, training the RBF layer unsupervised and a perceptron layer supervised. Results show the network accurately clustered most iris flowers into the three expected categories when trained on the iris data set.
Radial basis function network ppt bySheetal,Samreen and Dhanashrisheetal katkar
Radial Basis Functions are nonlinear activation functions used by artificial neural networks.Explained commonly used RBFs ,cover's theorem,interpolation problem and learning strategies.
The document discusses the Least-Mean Square (LMS) algorithm. It begins by introducing LMS as the first linear adaptive filtering algorithm developed by Widrow and Hoff in 1960. It then describes the filtering structure of LMS, modeling an unknown dynamic system using a linear neuron model and adjusting weights based on an error signal. Finally, it summarizes the LMS algorithm, outlines its virtues like computational simplicity and robustness, and notes its primary limitation is slow convergence for high-dimensional problems.
This document provides an overview of multilayer perceptrons (MLPs) and the backpropagation algorithm. It defines MLPs as neural networks with multiple hidden layers that can solve nonlinear problems. The backpropagation algorithm is introduced as a method for training MLPs by propagating error signals backward from the output to inner layers. Key steps include calculating the error at each neuron, determining the gradient to update weights, and using this to minimize overall network error through iterative weight adjustment.
The document provides an overview of convolutional neural networks (CNNs) and their layers. It begins with an introduction to CNNs, noting they are a type of neural network designed to process 2D inputs like images. It then discusses the typical CNN architecture of convolutional layers followed by pooling and fully connected layers. The document explains how CNNs work using a simple example of classifying handwritten X and O characters. It provides details on the different layer types, including convolutional layers which identify patterns using small filters, and pooling layers which downsample the inputs.
The document provides an overview of perceptrons and neural networks. It discusses how neural networks are modeled after the human brain and consist of interconnected artificial neurons. The key aspects covered include the McCulloch-Pitts neuron model, Rosenblatt's perceptron, different types of learning (supervised, unsupervised, reinforcement), the backpropagation algorithm, and applications of neural networks such as pattern recognition and machine translation.
In this presentation, we approach a two-class classification problem. We try to find a plane that separates the class in the feature space, also called a hyperplane. If we can't find a hyperplane, then we can be creative in two ways: 1) We soften what we mean by separate, and 2) We enrich and enlarge the featured space so that separation is possible.
Neural Networks for Pattern RecognitionVipra Singh
- Neural networks are computing systems inspired by biological neural networks in the brain that can be used for pattern recognition. An artificial neuron receives multiple inputs and produces a single output. Neural networks are trained to recognize complex patterns and identify categories.
- An important application of neural networks is pattern recognition, where a network is trained to associate input patterns with output categories. Recent advances include using neural networks for tasks like predicting student performance, medical diagnosis, and analyzing customer interactions. Neural networks are also being used increasingly in business for applications like predictive analytics and artificial intelligence.
The document describes multilayer neural networks and their use for classification problems. It discusses how neural networks can handle continuous-valued inputs and outputs unlike decision trees. Neural networks are inherently parallel and can be sped up through parallelization techniques. The document then provides details on the basic components of neural networks, including neurons, weights, biases, and activation functions. It also describes common network architectures like feedforward networks and discusses backpropagation for training networks.
Radial basis function network ppt bySheetal,Samreen and Dhanashrisheetal katkar
Radial Basis Functions are nonlinear activation functions used by artificial neural networks.Explained commonly used RBFs ,cover's theorem,interpolation problem and learning strategies.
The document discusses the Least-Mean Square (LMS) algorithm. It begins by introducing LMS as the first linear adaptive filtering algorithm developed by Widrow and Hoff in 1960. It then describes the filtering structure of LMS, modeling an unknown dynamic system using a linear neuron model and adjusting weights based on an error signal. Finally, it summarizes the LMS algorithm, outlines its virtues like computational simplicity and robustness, and notes its primary limitation is slow convergence for high-dimensional problems.
This document provides an overview of multilayer perceptrons (MLPs) and the backpropagation algorithm. It defines MLPs as neural networks with multiple hidden layers that can solve nonlinear problems. The backpropagation algorithm is introduced as a method for training MLPs by propagating error signals backward from the output to inner layers. Key steps include calculating the error at each neuron, determining the gradient to update weights, and using this to minimize overall network error through iterative weight adjustment.
The document provides an overview of convolutional neural networks (CNNs) and their layers. It begins with an introduction to CNNs, noting they are a type of neural network designed to process 2D inputs like images. It then discusses the typical CNN architecture of convolutional layers followed by pooling and fully connected layers. The document explains how CNNs work using a simple example of classifying handwritten X and O characters. It provides details on the different layer types, including convolutional layers which identify patterns using small filters, and pooling layers which downsample the inputs.
The document provides an overview of perceptrons and neural networks. It discusses how neural networks are modeled after the human brain and consist of interconnected artificial neurons. The key aspects covered include the McCulloch-Pitts neuron model, Rosenblatt's perceptron, different types of learning (supervised, unsupervised, reinforcement), the backpropagation algorithm, and applications of neural networks such as pattern recognition and machine translation.
In this presentation, we approach a two-class classification problem. We try to find a plane that separates the class in the feature space, also called a hyperplane. If we can't find a hyperplane, then we can be creative in two ways: 1) We soften what we mean by separate, and 2) We enrich and enlarge the featured space so that separation is possible.
Neural Networks for Pattern RecognitionVipra Singh
- Neural networks are computing systems inspired by biological neural networks in the brain that can be used for pattern recognition. An artificial neuron receives multiple inputs and produces a single output. Neural networks are trained to recognize complex patterns and identify categories.
- An important application of neural networks is pattern recognition, where a network is trained to associate input patterns with output categories. Recent advances include using neural networks for tasks like predicting student performance, medical diagnosis, and analyzing customer interactions. Neural networks are also being used increasingly in business for applications like predictive analytics and artificial intelligence.
The document describes multilayer neural networks and their use for classification problems. It discusses how neural networks can handle continuous-valued inputs and outputs unlike decision trees. Neural networks are inherently parallel and can be sped up through parallelization techniques. The document then provides details on the basic components of neural networks, including neurons, weights, biases, and activation functions. It also describes common network architectures like feedforward networks and discusses backpropagation for training networks.
This document provides an overview of self-organizing maps (SOM) as an unsupervised learning technique. It discusses the principles of self-organization including self-amplification, competition, and cooperation. The Willshaw-von der Malsburg model and Kohonen feature maps are presented as two approaches to building topographic maps through self-organization. The Kohonen SOM learning algorithm is described as involving competition between neurons to determine a winning neuron, cooperation between neighboring neurons, and adaptive changes to synaptic weights based on Hebbian learning principles.
Convolutional Neural Network - CNN | How CNN Works | Deep Learning Course | S...Simplilearn
A Convolutional Neural Network (CNN) is a type of neural network that can process grid-like data like images. It works by applying filters to the input image to extract features at different levels of abstraction. The CNN takes the pixel values of an input image as the input layer. Hidden layers like the convolution layer, ReLU layer and pooling layer are applied to extract features from the image. The fully connected layer at the end identifies the object in the image based on the extracted features. CNNs use the convolution operation with small filter matrices that are convolved across the width and height of the input volume to compute feature maps.
- Naive Bayes is a classification technique based on Bayes' theorem that uses "naive" independence assumptions. It is easy to build and can perform well even with large datasets.
- It works by calculating the posterior probability for each class given predictor values using the Bayes theorem and independence assumptions between predictors. The class with the highest posterior probability is predicted.
- It is commonly used for text classification, spam filtering, and sentiment analysis due to its fast performance and high success rates compared to other algorithms.
The presentation is made on CNN's which is explained using the image classification problem, the presentation was prepared in perspective of understanding computer vision and its applications. I tried to explain the CNN in the most simple way possible as for my understanding. This presentation helps the beginners of CNN to have a brief idea about the architecture and different layers in the architecture of CNN with the example. Please do refer the references in the last slide for a better idea on working of CNN. In this presentation, I have also discussed the different types of CNN(not all) and the applications of Computer Vision.
Convolutional neural networks (CNNs) learn multi-level features and perform classification jointly and better than traditional approaches for image classification and segmentation problems. CNNs have four main components: convolution, nonlinearity, pooling, and fully connected layers. Convolution extracts features from the input image using filters. Nonlinearity introduces nonlinearity. Pooling reduces dimensionality while retaining important information. The fully connected layer uses high-level features for classification. CNNs are trained end-to-end using backpropagation to minimize output errors by updating weights.
Backpropagation And Gradient Descent In Neural Networks | Neural Network Tuto...Simplilearn
This presentation about backpropagation and gradient descent will cover the basics of how backpropagation and gradient descent plays a role in training neural networks - using an example on how to recognize the handwritten digits using a neural network. After predicting the results, you will see how to train the network using backpropagation to obtain the results with high accuracy. Backpropagation is the process of updating the parameters of a network to reduce the error in prediction. You will also understand how to calculate the loss function to measure the error in the model. Finally, you will see with the help of a graph, how to find the minimum of a function using gradient descent. Now, let’s get started with learning backpropagation and gradient descent in neural networks.
Why Deep Learning?
It is one of the most popular software platforms used for deep learning and contains powerful tools to help you build and implement artificial neural networks.
Advancements in deep learning are being seen in smartphone applications, creating efficiencies in the power grid, driving advancements in healthcare, improving agricultural yields, and helping us find solutions to climate change. With this Tensorflow course, you’ll build expertise in deep learning models, learn to operate TensorFlow to manage neural networks and interpret the results.
And according to payscale.com, the median salary for engineers with deep learning skills tops $120,000 per year.
You can gain in-depth knowledge of Deep Learning by taking our Deep Learning certification training course. With Simplilearn’s Deep Learning course, you will prepare for a career as a Deep Learning engineer as you master concepts and techniques including supervised and unsupervised learning, mathematical and heuristic aspects, and hands-on modeling to develop algorithms. Those who complete the course will be able to:
1. Understand the concepts of TensorFlow, its main functions, operations and the execution pipeline
2. Implement deep learning algorithms, understand neural networks and traverse the layers of data abstraction which will empower you to understand data like never before
3. Master and comprehend advanced topics such as convolutional neural networks, recurrent neural networks, training deep networks and high-level interfaces
4. Build deep learning models in TensorFlow and interpret the results
5. Understand the language and fundamental concepts of artificial neural networks
6. Troubleshoot and improve deep learning models
7. Build your own deep learning project
8. Differentiate between machine learning, deep learning, and artificial intelligence
Learn more at https://www.simplilearn.com/deep-learning-course-with-tensorflow-training
- In 1975, Kunihiko Fukushima introduced the Cognitron network, which was an extension of the original perceptron and was able to handle pattern recognition problems better than the perceptron.
- The Cognitron used multiple layers of convergent subcircuits that allowed it to discriminate between patterns to some degree, unlike the perceptron.
- Fukushima later modified the Cognitron into the Neocognitron in 1980 by adding additional summation nodes, which made the network able to recognize patterns regardless of their position in the visual field.
The document discusses various neural network learning rules:
1. Error correction learning rule (delta rule) adapts weights based on the error between the actual and desired output.
2. Memory-based learning stores all training examples and classifies new inputs based on similarity to nearby examples (e.g. k-nearest neighbors).
3. Hebbian learning increases weights of simultaneously active neuron connections and decreases others, allowing patterns to emerge from correlations in inputs over time.
4. Competitive learning (winner-take-all) adapts the weights of the neuron most active for a given input, allowing unsupervised clustering of similar inputs across neurons.
The document discusses artificial neural networks. It describes their basic structure and components, including dendrites that receive input signals, a soma that processes the inputs, and an axon that transmits output signals. It also explains how neurons are connected at synapses to transfer signals between neurons. Finally, it mentions different types of activation functions that can be used in neural networks.
Basic definitions, terminologies, and Working of ANN has been explained. This ppt also shows how ANN can be performed in matlab. This material contains the explanation of Feed forward back propagation algorithm in detail.
Residual neural networks (ResNets) solve the vanishing gradient problem through shortcut connections that allow gradients to flow directly through the network. The ResNet architecture consists of repeating blocks with convolutional layers and shortcut connections. These connections perform identity mappings and add the outputs of the convolutional layers to the shortcut connection. This helps networks converge earlier and increases accuracy. Variants include basic blocks with two convolutional layers and bottleneck blocks with three layers. Parameters like number of layers affect ResNet performance, with deeper networks showing improved accuracy. YOLO is a variant that replaces the softmax layer with a 1x1 convolutional layer and logistic function for multi-label classification.
This document discusses feature extraction and selection methods for principal component analysis. It provides an introduction to principal component analysis and how it can be used for dimensionality reduction by transforming correlated variables into a set of uncorrelated variables. The document serves as a tutorial on feature extraction, selection, and principal component analysis.
Deep learning lecture - part 1 (basics, CNN)SungminYou
This presentation is a lecture with the Deep Learning book. (Bengio, Yoshua, Ian Goodfellow, and Aaron Courville. MIT press, 2017) It contains the basics of deep learning and theories about the convolutional neural network.
This document provides an overview of self-organizing maps (SOM) as an unsupervised learning technique. It discusses the principles of self-organization including self-amplification, competition, and cooperation. The Willshaw-von der Malsburg model and Kohonen feature maps are presented as two approaches to building topographic maps through self-organization. The Kohonen SOM learning algorithm is described as involving competition between neurons to determine a winning neuron, cooperation between neighboring neurons, and adaptive changes to synaptic weights based on Hebbian learning principles.
Convolutional Neural Network - CNN | How CNN Works | Deep Learning Course | S...Simplilearn
A Convolutional Neural Network (CNN) is a type of neural network that can process grid-like data like images. It works by applying filters to the input image to extract features at different levels of abstraction. The CNN takes the pixel values of an input image as the input layer. Hidden layers like the convolution layer, ReLU layer and pooling layer are applied to extract features from the image. The fully connected layer at the end identifies the object in the image based on the extracted features. CNNs use the convolution operation with small filter matrices that are convolved across the width and height of the input volume to compute feature maps.
- Naive Bayes is a classification technique based on Bayes' theorem that uses "naive" independence assumptions. It is easy to build and can perform well even with large datasets.
- It works by calculating the posterior probability for each class given predictor values using the Bayes theorem and independence assumptions between predictors. The class with the highest posterior probability is predicted.
- It is commonly used for text classification, spam filtering, and sentiment analysis due to its fast performance and high success rates compared to other algorithms.
The presentation is made on CNN's which is explained using the image classification problem, the presentation was prepared in perspective of understanding computer vision and its applications. I tried to explain the CNN in the most simple way possible as for my understanding. This presentation helps the beginners of CNN to have a brief idea about the architecture and different layers in the architecture of CNN with the example. Please do refer the references in the last slide for a better idea on working of CNN. In this presentation, I have also discussed the different types of CNN(not all) and the applications of Computer Vision.
Convolutional neural networks (CNNs) learn multi-level features and perform classification jointly and better than traditional approaches for image classification and segmentation problems. CNNs have four main components: convolution, nonlinearity, pooling, and fully connected layers. Convolution extracts features from the input image using filters. Nonlinearity introduces nonlinearity. Pooling reduces dimensionality while retaining important information. The fully connected layer uses high-level features for classification. CNNs are trained end-to-end using backpropagation to minimize output errors by updating weights.
Backpropagation And Gradient Descent In Neural Networks | Neural Network Tuto...Simplilearn
This presentation about backpropagation and gradient descent will cover the basics of how backpropagation and gradient descent plays a role in training neural networks - using an example on how to recognize the handwritten digits using a neural network. After predicting the results, you will see how to train the network using backpropagation to obtain the results with high accuracy. Backpropagation is the process of updating the parameters of a network to reduce the error in prediction. You will also understand how to calculate the loss function to measure the error in the model. Finally, you will see with the help of a graph, how to find the minimum of a function using gradient descent. Now, let’s get started with learning backpropagation and gradient descent in neural networks.
Why Deep Learning?
It is one of the most popular software platforms used for deep learning and contains powerful tools to help you build and implement artificial neural networks.
Advancements in deep learning are being seen in smartphone applications, creating efficiencies in the power grid, driving advancements in healthcare, improving agricultural yields, and helping us find solutions to climate change. With this Tensorflow course, you’ll build expertise in deep learning models, learn to operate TensorFlow to manage neural networks and interpret the results.
And according to payscale.com, the median salary for engineers with deep learning skills tops $120,000 per year.
You can gain in-depth knowledge of Deep Learning by taking our Deep Learning certification training course. With Simplilearn’s Deep Learning course, you will prepare for a career as a Deep Learning engineer as you master concepts and techniques including supervised and unsupervised learning, mathematical and heuristic aspects, and hands-on modeling to develop algorithms. Those who complete the course will be able to:
1. Understand the concepts of TensorFlow, its main functions, operations and the execution pipeline
2. Implement deep learning algorithms, understand neural networks and traverse the layers of data abstraction which will empower you to understand data like never before
3. Master and comprehend advanced topics such as convolutional neural networks, recurrent neural networks, training deep networks and high-level interfaces
4. Build deep learning models in TensorFlow and interpret the results
5. Understand the language and fundamental concepts of artificial neural networks
6. Troubleshoot and improve deep learning models
7. Build your own deep learning project
8. Differentiate between machine learning, deep learning, and artificial intelligence
Learn more at https://www.simplilearn.com/deep-learning-course-with-tensorflow-training
- In 1975, Kunihiko Fukushima introduced the Cognitron network, which was an extension of the original perceptron and was able to handle pattern recognition problems better than the perceptron.
- The Cognitron used multiple layers of convergent subcircuits that allowed it to discriminate between patterns to some degree, unlike the perceptron.
- Fukushima later modified the Cognitron into the Neocognitron in 1980 by adding additional summation nodes, which made the network able to recognize patterns regardless of their position in the visual field.
The document discusses various neural network learning rules:
1. Error correction learning rule (delta rule) adapts weights based on the error between the actual and desired output.
2. Memory-based learning stores all training examples and classifies new inputs based on similarity to nearby examples (e.g. k-nearest neighbors).
3. Hebbian learning increases weights of simultaneously active neuron connections and decreases others, allowing patterns to emerge from correlations in inputs over time.
4. Competitive learning (winner-take-all) adapts the weights of the neuron most active for a given input, allowing unsupervised clustering of similar inputs across neurons.
The document discusses artificial neural networks. It describes their basic structure and components, including dendrites that receive input signals, a soma that processes the inputs, and an axon that transmits output signals. It also explains how neurons are connected at synapses to transfer signals between neurons. Finally, it mentions different types of activation functions that can be used in neural networks.
Basic definitions, terminologies, and Working of ANN has been explained. This ppt also shows how ANN can be performed in matlab. This material contains the explanation of Feed forward back propagation algorithm in detail.
Residual neural networks (ResNets) solve the vanishing gradient problem through shortcut connections that allow gradients to flow directly through the network. The ResNet architecture consists of repeating blocks with convolutional layers and shortcut connections. These connections perform identity mappings and add the outputs of the convolutional layers to the shortcut connection. This helps networks converge earlier and increases accuracy. Variants include basic blocks with two convolutional layers and bottleneck blocks with three layers. Parameters like number of layers affect ResNet performance, with deeper networks showing improved accuracy. YOLO is a variant that replaces the softmax layer with a 1x1 convolutional layer and logistic function for multi-label classification.
This document discusses feature extraction and selection methods for principal component analysis. It provides an introduction to principal component analysis and how it can be used for dimensionality reduction by transforming correlated variables into a set of uncorrelated variables. The document serves as a tutorial on feature extraction, selection, and principal component analysis.
Deep learning lecture - part 1 (basics, CNN)SungminYou
This presentation is a lecture with the Deep Learning book. (Bengio, Yoshua, Ian Goodfellow, and Aaron Courville. MIT press, 2017) It contains the basics of deep learning and theories about the convolutional neural network.
This document discusses kernel methods and radial basis function (RBF) networks. It begins with an introduction and overview of Cover's theory of separability of patterns. It then revisits the XOR problem and shows how it can be solved using Gaussian hidden functions. The interpolation problem is explained and how RBF networks can perform strict interpolation through a set of training data points. Radial basis functions that satisfy Micchelli's theorem allowing for a nonsingular interpolation matrix are presented. Finally, the structure and training of RBF networks using k-means clustering and recursive least squares estimation is covered.
Introduction to Radial Basis Function NetworksESCOM
This document provides an introduction to radial basis function (RBF) networks, a type of artificial neural network used for supervised learning problems. It describes how RBF networks are a type of linear model that uses radial basis functions as activation functions for hidden units. While RBF networks are nonlinear, the document emphasizes keeping the underlying mathematics and computations linear to simplify the problem and reduce computational costs compared to other neural network techniques that rely on nonlinear optimization algorithms. It reviews key concepts for RBF networks like least squares optimization, model selection, ridge regression, and forward selection techniques for building networks from data.
The document summarizes radial basis function (RBF) networks. Key points:
- RBF networks use radial basis functions as activation functions and can universally approximate continuous functions.
- They are local approximators compared to multilayer perceptrons which are global approximators.
- Learning involves determining the centers, widths, and weights. Centers can be randomly selected or via clustering. Widths are usually different for each basis function. Weights are typically learned via least squares or gradient descent methods.
This document provides an introduction to radial basis function (RBF) interpolation of scattered data. It discusses how RBFs choose basis functions centered at data points to guarantee a well-posed interpolation problem. Common RBF kernels include the multiquadric, inverse multiquadric, and Gaussian functions. While RBF interpolation is guaranteed to have a unique solution, it can still be ill-conditioned depending on the shape parameter choice. Considerations for using RBFs include that the interpolation matrix is dense, requiring optimization of the shape parameter, and interpolation error increases near boundaries.
Recognition of handwritten digits using rbf neural networkeSAT Journals
Abstract Pattern recognition is required in many fields for different purposes. Methods based on Radial basis function (RBF) neural networks are found to be very successful in pattern classification problems. Training neural network is in general a challenging nonlinear optimization problem. Several algorithms have been proposed for choosing the RBF neural network prototypes and training the network. In this paper RBF neural network using decoupling Kalman filter method is proposed for handwritten digit recognition applications. The efficacy of the proposed method is tested on the handwritten digits of different fonts and found that it is successful in recognizing the digits. Keywords: - Neural network, RBF neural network, Decoupled kalman filter Training, Zoning method
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Wireless Positioning using Ellipsoidal ConstraintsGiovanni Soldi
This master's thesis presents a new approach for indoor positioning, based on the notion of separating ellipsoids. In order to improve the position estimation algorithm, the technique is combined with the algorithm A*, being applied to binary maps of the examined buildings to take into account obstacles such as walls.
The combination of separating ellipsoids and A seems to promise an improvement over previous algorithms based on a probabilistic approaches.
This document discusses hardware architectures for deep learning and exploiting sparsity. It covers three key topics:
1) Exploiting sparsity in deep neural networks to reduce operations and storage requirements, such as sparsity from ReLU activations and pruning weights. This can reduce data movement and the number of operations.
2) Methods for exploiting sparsity, including compressing sparse data, skipping zero activations, pruning small activations, and exploiting spatial/temporal correlations. Pruning techniques like magnitude-based and sensitivity-based pruning are also covered.
3) The benefits of sparsity for different hardware architectures, such as graph neural networks where the graph representation is often sparse, allowing for reductions in data movement and storage.
An efficient technique for color image classification based on lower feature ...Alexander Decker
This document discusses an efficient technique for color image classification using support vector machines with radial basis functions (SVM-RBF). It presents SVM-RBF as an improvement over other classification methods like SVM with ant colony optimization (SVM-ACO) and directed acyclic graph (SVM-DAG). The paper tests the different classifiers on 600 images across 3 classes, finding SVM-RBF achieved the highest precision and recall rates, with precision of 92.3-94% and recall of 84.8-91%. It concludes SVM-RBF more effectively reduces noise and the semantic gap to enhance image classification performance compared to the other methods.
Ml srhwt-machine-learning-based-superlative-rapid-haar-wavelet-transformation...Jumlesha Shaik
Abstract: In this paper a digital image coding technique called ML-SRHWT (Machine Learning based image coding by Superlative Rapid HAAR Wavelet Transform) has been introduced. Compression of digital image is done using the model Superlative Rapid HAAR Wavelet Transform (SRHWT). The Least Square Support vector Machine regression predicts hyper coefficients obtained by using QPSO model. The mathematical models are discussed in brief in this paper are SRHWT, which results in good performance and reduces the complexity compared to FHAAR and EQPSO by replacing the least good particle with the new best obtained particle in QPSO. On comparing the ML-SRHWT with JPEG and JPEG2000 standards, the former is considered to be the better.
IRJET- Clustering the Real Time Moving Object Adjacent TrackingIRJET Journal
This paper proposes a new algorithm for clustering the trajectories of moving objects in real-time based on sensor data. The algorithm represents each object's trajectory as a series of time-stamped positions. It aims to reduce data storage and transmission costs by clustering objects with similar movements together and sending updates only when objects change clusters. The key aspects of the algorithm are using a metric called M that measures how well an object fits in a cluster based on its predicted future trajectory, and updating clusters and transmitting changes when this metric exceeds a threshold for an object.
This document summarizes a research paper that proposes a Virtual Backbone Scheduling technique with clustering and fuzzy logic for faster data collection in wireless sensor networks. It introduces the concepts of virtual backbone scheduling, clustering, and fuzzy logic. It presents the system architecture that uses these techniques and includes three clusters with sensor nodes, cluster heads, and a common sink node. Algorithms for virtual backbone scheduling and fuzzy-based clustering are described. Implementation results show that the proposed approach improves network lifetime, reduces error rates, lowers communication costs, and decreases scheduling time compared to existing techniques like TDMA scheduling.
Hybrid nearest neighbour and feed forward neural networks algorithm for indoo...Conference Papers
This document presents a hybrid algorithm for indoor positioning systems that combines k-nearest neighbors (kNN) and feed-forward neural networks (FNNs). The algorithm uses received signal strength (RSS) from WiFi access points as input. It was found that a basic kNN algorithm achieved better median and minimum error distances than FNNs alone. A hybrid kNN-FNNs algorithm trained with a metaheuristic algorithm called stochastic fractal search further improved accuracy, achieving an error of less than 5 meters in 86.39% of cases compared to 69.67% for basic kNN. The hybrid approach combines the strengths of the individual algorithms to provide more accurate indoor positioning estimation.
Support Vector Machine Optimal Kernel SelectionIRJET Journal
This document discusses selecting the optimal kernel for support vector machines (SVMs) based on different datasets. It provides background on SVMs and how their performance depends on the kernel function used. The document evaluates 4 kernel types (linear, polynomial, radial basis function (RBF), sigmoid) on 3 datasets: heart disease data, digit recognition data, and social network ads data. For each dataset and kernel combination, it reports accuracy, sensitivity, specificity, and kappa statistic metrics from implementing SVMs in R. The linear and RBF kernels generally performed best, with RBF working best for datasets with larger numbers of features like digit recognition data.
Particle Swarm Optimization Based QoS Aware Routing for Wireless Sensor Networksijsrd.com
Efficiency in a Wireless Sensor Network can only be obtained with effective routing mechanisms. This paper uses Particle Swarm Optimization (PSO, a metaheuristic algorithm to perform the process of routing. Since PSO does not have a defined fitness function, it is flexible to incorporate user defined QoS parameters to define the fitness function.
PSO-based Training, Pruning, and Ensembling of Extreme Learning Machine RBF N...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
This document discusses deep neural networks and computational graphs. It begins by explaining key concepts like derivatives, partial derivatives, optimization, training sets, and activation functions. It then provides examples of applying the chain rule in deep learning, including forward and back propagation in a neural network. Specifically, it demonstrates forward propagation through a simple network and calculating the gradient using backpropagation and the chain rule. Finally, it works through an example applying these concepts to a neural network using sigmoid activation functions.
Robust Adaptive Threshold Algorithm based on Kernel Fuzzy Clustering on Image...cscpconf
The document presents a robust adaptive threshold algorithm based on kernel fuzzy clustering for image segmentation. It proposes using kernel fuzzy c-means clustering (KFCM) to generate adaptive thresholds for segmenting images. KFCM computes fuzzy membership values for pixels to cluster them. The algorithm was tested on MR brain images and showed good performance in detecting large and small objects while also enhancing low contrast images. Experimental results demonstrated the efficiency and accuracy of combining an adaptive threshold algorithm with KFCM for medical image segmentation.
As Wireless Sensor Networks are penetrating into the industrial domain, many research opportunities are emerging. One such essential and challenging application is that of node localization. A feed-forward neural network based methodology is adopted in this paper. The Received Signal Strength Indicator (RSSI) values of the anchor node beacons are used. The number of anchor nodes and their configurations has an impact on the accuracy of the localization system, which is also addressed in this paper. Five different training algorithms are evaluated to find the training algorithm that gives the best result. The multi-layer Perceptron (MLP) neural network model was trained using Matlab. In order to evaluate the performance of the proposed method in real time, the model obtained was then implemented on the Arduino microcontroller. With four anchor nodes, an average 2D localization error of 0.2953 m has been achieved with a 12-12-2 neural network structure. The proposed method can also be implemented on any other embedded microcontroller system.
The document presents research on using neural networks to predict Earth Orientation Parameters (EOP) such as UT1-TAI. Three neural network models were tested:
1) Network 1 varied the number of neurons proportionally with increasing training sample size.
2) Network 2 kept the number of neurons constant while increasing sample size.
3) Network 3 used daily training data with 2 neurons and sample sizes of 4, 10, 20, and 365 days.
The goal was to minimize prediction error (RMSE) for horizons of 5-25 days by adjusting sample size and neurons. Results showed the best balance was needed between these factors, and that short-term prediction was possible within 10 days using
CSC 347 – Computer Hardware and MaintenanceSumaiya Ismail
This is report format on CSC 347 – Computer Hardware and Maintenance. It is for IUBAT university but as per I assume every University can use this format.
Redundant Actor Based Multi-Hole Healing System for Mobile Sensor NetworksEditor IJCATR
In recent years, the Mobile Wireless Sensor Network
is the emerging solution for monitoring of a specified region of
interest. Several anomalies can occur in WSNs that impair their
desired functionalities resulting in the formation of different
kinds of holes, namely: coverage holes, routing holes. Our
ultimate aim is to cover total area without coverage hole in
wireless sensor networks. We propose a comprehensive solution,
called holes detection and healing. We divided our proposed
work into two phases. The first phase consists of three sub- tasks;
Hole-identification, Hole-discovery and border detection. The
second phase treats the Hole-healing with novel concept, hole
healing area. It consists of two sub-tasks; Hole healing area
determination and node relocation.
Localization based range map stitching in wireless sensor network under non l...eSAT Publishing House
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Radial Basis Function
1. CSC 367 2.0 Mathematical Computing
Assignment 3
Radial Basis Functions
AS2010377
M.K.H.Gunasekara
Special Part 1
Department of Computer Science
UNIVERSITY OF SRI JAYEWARDENEPURA
3. M.K.H.Gunasekara - AS2010377
CSC 367 2.0 Mathematical Computing
Introduction
Neural Networks offer a powerful framework for representing nonlinear mappings from
several inputs to one or more outputs.
An important application of neural networks is regression. Instead of mapping the inputs
into a discrete class label, the neural network maps the input variables into continuous
values. A major class of neural networks is the radial basis function (RBF) neural network.
We will look at the architecture of RBF neural networks, followed by its applications in both
regression and classification.
In this report Radial Basis function is discussed for clustering as unsupervised learning
algorithm. Radial basis function is simulated to cluster three flowers in a given data set
which is available in http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data.
2|Page
4. M.K.H.Gunasekara - AS2010377
CSC 367 2.0 Mathematical Computing
Methodology
Radial Basis Function
Figure 01 : One hidden layer with Radial Basis Activation Functions
Radial basis function (RBF) networks typically have three layers
1. Input Layer
2. A hidden layer with a non-linear RBF activation function
3. Output Layer
Where N is the number of neurons in the hidden layer,
is the center vector for neuron i, and is
the weight of neuron i in the linear output neuron. Functions that depend only on the distance from
a center vector are radially symmetric about that vector, hence the name radial basis function. In the
basic form all inputs are connected to each hidden neuron. The norm is typically taken to be the
Euclidean distance and the radial basis function is commonly taken to be Gaussian Function
(
)
(
‖
‖
)
------ (1)
There are some other Radial Basis functions
Logistic Basis Function
( )
( )
Multi-quadratics
( )
√
3|Page
5. M.K.H.Gunasekara - AS2010377
CSC 367 2.0 Mathematical Computing
Input nodes connected by weights to a set of RBF neurons fire proportionately to the distance
between the input and the neuron in the weight space
The activation of these nodes is used as inputs to the second layer. The second layer (output layer) is
treated as a simple Perceptron network
Training the RBF Network
This can be done positioning the RBF nodes and using the activation of RBF nodes to train the linear
outputs.
Positioning RBF nodes can be done in two ways; First method is randomly picking some of the data
points to act as basis functions. And the second method is trying to position the nodes so that they
are representative of typical inputs, like using k-means clustering algorithm.
In Activation function there is standard deviation parameter.
One option is, giving all nodes the same size, and testing lots of different sizes using a validation set
to select one that works. Alternatively we can select the size of RBF nodes so that the whole space is
coved by the receptive fields. So the width of the Gaussian should be set according to the maximum
distance between the locations of the hidden nodes (d), and the number of hidden nodes (M)
------ (2)
√
We can use this normalized Gaussian function also.
(
‖
(
)
∑
(
‖
‖
)
‖
------ (3)
)
Outputs of the RBF Network:
(
‖
‖
)
Training the Perceptron Network
We can train Pereceptron Network by using supervised learning method. Therefore we train the
MLP Network according to targets.
4|Page
6. M.K.H.Gunasekara - AS2010377
CSC 367 2.0 Mathematical Computing
Implementation
Implementation was done using MATLAB 7.10 (2010). Implementation was done according to
following methods
1.
2.
3.
4.
5.
Locate RBF nodes into centers
Calculate for the Gaussian function
Calculate outputs of the RBF layer – Unsupervised Training
Make Perceptron Network for second layer –( I used MLP network without a hidden layer)
Train MLP Network according to targets and inputs (inputs are the output of RBF network) –
Supervised Training
6. Simulate the network
I have implement RBF Network with different strategies to compare the results
Using Randomly selected centers
Using K-Means Cluster centers
Using Non-normalized Gaussian function
Using Normalized Gaussian function
Using SVM for second layer
5|Page
10. M.K.H.Gunasekara - AS2010377
6.7
7.2
6.2
6.1
6.4
7.2
7.4
7.9
6.4
6.3
6.1
7.7
6.3
6.4
6
6.9
6.7
6.9
5.8
6.8
6.7
6.7
6.3
6.5
6.2
5.9
3.3
3.2
2.8
3
2.8
3
2.8
3.8
2.8
2.8
2.6
3
3.4
3.1
3
3.1
3.1
3.1
2.7
3.2
3.3
3
2.5
3
3.4
3
CSC 367 2.0 Mathematical Computing
5.7
6
4.8
4.9
5.6
5.8
6.1
6.4
5.6
5.1
5.6
6.1
5.6
5.5
4.8
5.4
5.6
5.1
5.1
5.9
5.7
5.2
5
5.2
5.4
5.1
2.1
1.8
1.8
1.8
2.1
1.6
1.9
2
2.2
1.5
1.4
2.3
2.4
1.8
1.8
2.1
2.4
2.3
1.9
2.3
2.5
2.3
1.9
2
2.3
1.8
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
FALSE
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
Iris-virginica
I found best results using RBF Network with Non-Normalized Gaussian activation function with 9
mismatches. And I found best results using MLP Network with 4 mismatches.
MLP Network as Second Layer
Non-Normalized Gaussian
function
Normalized Gaussian function
Random Center
9
K Means Center
9
11
11
Support Vector Machine as Second Layer
Non-Normalized Gaussian
function
Normalized Gaussian function
9|Page
Random Center
14
K Means Center
10
14
17
11. M.K.H.Gunasekara - AS2010377
CSC 367 2.0 Mathematical Computing
Discussion
1. There are some drawbacks of unsupervised center selection in radial basis functions
2. We can use an SVM for the second layer instead of a perceptron but it is not efficient for more
than 2 classes classification
10 | P a g e
12. M.K.H.Gunasekara - AS2010377
CSC 367 2.0 Mathematical Computing
Appendices
MATLAB Sourcecode for RBF Network with MLP Network
clc
clear all
% M.K.H. Gunasekara
% AS2010377
% Machine Learning
% Radial Basis Function
[arr tx] = xlsread('data.xls');
Centers=zeros(3,4);
% I found centers as mean of the same cluster values
for i=1:50
Centers(1,1)=arr(i,1)+Centers(1,1);
Centers(1,2)=arr(i,2)+Centers(1,2);
Centers(1,3)=arr(i,3)+Centers(1,3);
Centers(1,4)=arr(i,4)+Centers(1,4);
end
for i=51:100
Centers(2,1)=arr(i,1)+Centers(2,1);
Centers(2,2)=arr(i,2)+Centers(2,2);
Centers(2,3)=arr(i,3)+Centers(2,3);
Centers(2,4)=arr(i,4)+Centers(2,4);
end
for i=101:150
Centers(3,1)=arr(i,1)+Centers(3,1);
Centers(3,2)=arr(i,2)+Centers(3,2);
Centers(3,3)=arr(i,3)+Centers(3,3);
Centers(3,4)=arr(i,4)+Centers(3,4);
end
for j= 1:3
Centers(j,1)=Centers(j,1)/50;
Centers(j,2)=Centers(j,2)/50;
Centers(j,3)=Centers(j,3)/50;
Centers(j,4)=Centers(j,4)/50;
end
Centers
% OR we can use k means algorithms calculate cluster centers
k=3; %number of clusters
[IDX,C]=kmeans(arr,k);
C %RBF centres
%Uncomment following line to use k means
%Centers=C;
11 | P a g e
13. M.K.H.Gunasekara - AS2010377
CSC 367 2.0 Mathematical Computing
% distance between hidden nodes
%distance between hidden node 1 & 2
dist1= sqrt((Centers(1,1)-Centers(2,1))^2 + (Centers(1,2)-Centers(2,2))^2 +
(Centers(1,3)-Centers(2,3))^2 + (Centers(1,4)-Centers(2,4))^2);
%distance between hidden node 1 & 3
dist2= sqrt((Centers(1,1)-Centers(3,1))^2 + (Centers(1,2)-Centers(3,2))^2 +
(Centers(1,3)-Centers(3,3))^2 + (Centers(1,4)-Centers(3,4))^2);
%distance between hidden node 3 & 2
dist3= sqrt((Centers(3,1)-Centers(2,1))^2 + (Centers(3,2)-Centers(2,2))^2 +
(Centers(3,3)-Centers(2,3))^2 + (Centers(3,4)-Centers(2,4))^2);
% finding maximum distance
maxdist=0;
if ( dist1>dist2) & (dist1>dist3)
maxdist=dist1;
end
if ( dist2>dist1) & (dist2>dist3)
maxdist=dist2;
end
if ( dist3>dist1) & (dist3>dist2)
maxdist=dist3;
end
% calculating width
sigma= maxdist/sqrt(2*3);
maxdist;
% Gaussian
%calculating outputs of RBF networks
RBFoutput=zeros(150,3);
d1=zeros(1,4);
Centers;
d=zeros(1,3);
%Unnormalized method
% calculate output for gaussian function
%Uncomment following lines (98-106) to use Non-Normalized Activation
%functions
%
for i=1:150
for j=1:3
d(1,j)= (arr(i,1)- Centers(j,1))^2 + (arr(i,2)- Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4)- Centers(j,4))^2;
RBFoutput(i,j)= exp(-(d(1,j)/(2*(sigma^2))));
end
end
12 | P a g e
15. M.K.H.Gunasekara - AS2010377
CSC 367 2.0 Mathematical Computing
MLPnet.trainParam.perf = 'mse';
MLPnet.trainParam.goal = 0.001;
MLPnet.trainParam.min_grad = 0.00001;
MLPnet.trainParam.max_fail=4;
MLPnet = train(MLPnet,RBFo,T);
%simulating neural network
y=sim(MLPnet,RBFo);
output=round(y.');
Target=T.';
compare= [T.' output]
count=0;
for i=1:150
if(output(i)~=Target(i))
count=count+1;
end
end
Unmatched=count
MATLAB Source code for RBF Network with SVM
clc
clear all
% M.K.H. Gunasekara
% AS2010377
% Machine Learning
% Radial Basis Function with Support Vector Machine
[arr tx] = xlsread('data.xls');
Centers=zeros(3,4);
% I found centers as mean of the same cluster values
for i=1:50
Centers(1,1)=arr(i,1)+Centers(1,1);
Centers(1,2)=arr(i,2)+Centers(1,2);
Centers(1,3)=arr(i,3)+Centers(1,3);
Centers(1,4)=arr(i,4)+Centers(1,4);
end
for i=51:100
Centers(2,1)=arr(i,1)+Centers(2,1);
Centers(2,2)=arr(i,2)+Centers(2,2);
Centers(2,3)=arr(i,3)+Centers(2,3);
Centers(2,4)=arr(i,4)+Centers(2,4);
end
for i=101:150
Centers(3,1)=arr(i,1)+Centers(3,1);
Centers(3,2)=arr(i,2)+Centers(3,2);
Centers(3,3)=arr(i,3)+Centers(3,3);
14 | P a g e
16. M.K.H.Gunasekara - AS2010377
CSC 367 2.0 Mathematical Computing
Centers(3,4)=arr(i,4)+Centers(3,4);
end
for j= 1:3
Centers(j,1)=Centers(j,1)/50;
Centers(j,2)=Centers(j,2)/50;
Centers(j,3)=Centers(j,3)/50;
Centers(j,4)=Centers(j,4)/50;
end
Centers
% OR we can use k means algorithms calculate cluster centers
k=3; %number of clusters
[IDX,C]=kmeans(arr,k);
C %RBF centres
%Uncomment following line to use k means
Centers=C;
% distance between hidden nodes
%distance between hidden node 1 & 2
dist1= sqrt((Centers(1,1)-Centers(2,1))^2 + (Centers(1,2)-Centers(2,2))^2 +
(Centers(1,3)-Centers(2,3))^2 + (Centers(1,4)-Centers(2,4))^2);
%distance between hidden node 1 & 3
dist2= sqrt((Centers(1,1)-Centers(3,1))^2 + (Centers(1,2)-Centers(3,2))^2 +
(Centers(1,3)-Centers(3,3))^2 + (Centers(1,4)-Centers(3,4))^2);
%distance between hidden node 3 & 2
dist3= sqrt((Centers(3,1)-Centers(2,1))^2 + (Centers(3,2)-Centers(2,2))^2 +
(Centers(3,3)-Centers(2,3))^2 + (Centers(3,4)-Centers(2,4))^2);
% finding maximum distance
maxdist=0;
if ( dist1>dist2) & (dist1>dist3)
maxdist=dist1;
end
if ( dist2>dist1) & (dist2>dist3)
maxdist=dist2;
end
if ( dist3>dist1) & (dist3>dist2)
maxdist=dist3;
end
% calculating width
sigma= maxdist/sqrt(2*3);
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17. M.K.H.Gunasekara - AS2010377
CSC 367 2.0 Mathematical Computing
maxdist;
% Gaussian
%calculating outputs of RBF networks
RBFoutput=zeros(150,3);
d1=zeros(1,4);
Centers;
%Unnormalized method
% calculate output for gaussian function
%Uncomment following lines (98-106) to use Non-Normalized Activation
%functions
d=zeros(1,3);
for i=1:150
for j=1:3
d(1,j)= (arr(i,1)- Centers(j,1))^2 + (arr(i,2)- Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4)- Centers(j,4))^2;
RBFoutput(i,j)= exp(-(d(1,j)/(2*(sigma^2))));
end
% d=[0 0 0];
end
%
%Normalized method
%Summation
%Uncomment following lines (114-130) to use Gaussian Normalized Activation
functions
% RBFNormSum=zeros(150,1);
% for i=1:150
%
for j=1:3
%
d(1,j)= (arr(i,1)- Centers(j,1))^2 + (arr(i,2)- Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4)- Centers(j,4))^2;
%
RBFNormSum(i,1)= exp(-(d(1,j)/(2*(sigma^2))))+ RBFNormSum(i,1);
%
end
%
% d=[0 0 0];
% end
%
% % calculate output for gaussian function
% for i=1:150
%
for j=1:3
%
d(1,j)= (arr(i,1)- Centers(j,1))^2 + (arr(i,2)- Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4)- Centers(j,4))^2;
%
%
RBFoutput(i,j)= exp(-(d(1,j)/(2*(sigma^2))))/RBFNormSum(i,1);
%
end
%
% d=[0 0 0];
% end
RBFoutput
RBFo=RBFoutput.'
% making SVM network
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