Neural Network
A neural network is a computational model inspired by the structure and functioning of the human brain. It is a fundamental component of machine learning and artificial intelligence and is used for various tasks such as image recognition, natural language processing, and decision-making. Neural networks consist of interconnected nodes or artificial neurons organized into layers. Here's a basic description of the key components and concepts related to neural networks:
Neurons
Neurons (Nodes): Neurons are the basic building blocks of a neural network. Each neuron receives input, processes it, and produces an output. In an artificial neural network, neurons are mathematical functions that perform operations on input data.
Neurons, also known as nerve cells, are the fundamental building blocks of the nervous system in living organisms, including humans. These specialized cells play a critical role in transmitting electrical and chemical signals throughout the body, enabling various functions such as sensory perception, motor control, memory, and cognitive processes. In the context of artificial neural networks and machine learning, artificial neurons are modeled after biological neurons to perform mathematical computations.
Here's a description of both biological and artificial neurons:
Biological Neurons (Neurons in Living Organisms):
Cell Body (Soma): The cell body is the central part of a biological neuron. It contains the nucleus and other essential cellular components.
Dendrites: Dendrites are branch-like structures that extend from the cell body. They receive electrical signals (in the form of neurotransmitters) from other neurons or sensory receptors and transmit them toward the cell body.
Axon: The axon is a long, slender projection that extends from the cell body. It carries electrical signals, called action potentials, away from the cell body and toward other neurons or target cells.
Synapses: At the end of an axon, there are synapses, which are small gaps between neurons. Neurotransmitters are released into these synapses to transmit signals from one neuron to the next. This process is crucial for information transfer between neurons.
Action Potential: When a neuron receives a strong enough signal from its dendrites, it generates an action potential, which is a brief electrical impulse that travels down the axon to transmit information to other neurons.
Neurotransmitters: Chemical messengers called neurotransmitters are released at synapses to transmit signals between neurons. These neurotransmitters can either excite or inhibit the activity of the receiving neuron.
Artificial Neurons (Neurons in Neural Networks):
Input: Artificial neurons receive input values, which could represent features, data points, or activations from previous neurons in the network.
Weights: Each input is associated with a weight. These weights determine the strength of the connection between the input and the neuron. Weights are adjusted during the training process to enable the neuron to learn.
Bias: A bias term is added to the weighted sum of inputs. The bias allows the neuron to learn an offset or threshold, affecting the neuron's activation.
Activation Function: An activation function (e.g., sigmoid, ReLU, tanh) is applied to the weighted sum of inputs and bias. It introduces non-linearity into the artificial neuron's response and helps the network learn complex relationships.
Output: The output of an artificial neuron is the result of applying the activation function to the weighted sum of inputs and bias. This output is then passed as input to subsequent neurons in the network.
Artificial neurons are organized into layers within a neural network, and they work collectively to process information and make predictions or decisions. By adjusting the weights and biases during training, artificial neurons can learn to approximate complex functions and solve various machine-learning tasks, such as image classification, natural language processing, and regression. These artificial neurons collectively create the computational power of neural networks, allowing them to model complex patterns and relationships in data.
Layers: Neurons are organized into layers within a neural network. The most common types of layers are:
In a neural network, layers are a fundamental architectural component that organize and structure the computation of the network. Each layer consists of a collection of neurons, also known as nodes or units, which work together to process and transform data. Neural networks typically consist of several types of layers, including input layers, hidden layers, and output layers. Here's a description of each type of layer:
Input Layer: The first layer that receives the initial data or input features. The input layer is the first layer of a neural network.
Neurons in this layer simply pass the input data forward to the subsequent layers without any processing.
The number of neurons in the input layer is determined by the dimensionality of the input data. For example, in an image classification task, each neuron might correspond to a pixel or a feature of the image.
The input layer serves as the entry point for data into the neural network.
Hidden Layers: Intermediate layers between the input and output layers. These layers perform complex transformations on the input data. Hidden layers are intermediate layers in a neural network that exists between the input and output layers.
They are called "hidden" because their activations are not directly observable in the network's input or output.
Hidden layers perform complex computations on the data, transforming it into higher-level representations that help the network learn and extract meaningful features from the input.
The number of hidden layers and the number of neurons in each hidden layer are design choices that can significantly impact the network's performance and capacity to model complex patterns.
Output Layer: The final layer that produces the network's output, which can be a prediction or classification result.
The output layer is the final layer of a neural network.
The neurons in this layer produce the network's output, which can take various forms depending on the task. For instance, in a classification task, each neuron might represent a different class, and the neuron with the highest activation value indicates the predicted class.
The number of neurons in the output layer depends on the type of problem; for binary classification, there may be one neuron, while multi-class classification tasks may have multiple neurons.
The activation function used in the output layer depends on the problem, with common choices being softmax for classification tasks and linear activation for regression tasks.
Additionally, some neural network architectures incorporate specialized layers to address specific tasks or challenges:
Convolutional Layers (ConvNets):
Commonly used in computer vision tasks, convolutional layers are designed to extract spatial hierarchies of features from images or multidimensional data.
They utilize convolutional operations to scan and learn local patterns and structures within the data.
Recurrent Layers (RNNs and LSTMs):
Recurrent layers are used for sequential data, such as time series, natural language, and speech.
They maintain internal memory and process data in a sequential manner, making them suitable for tasks involving temporal dependencies.
Pooling Layers:
Often used in conjunction with convolutional layers, pooling layers downsample the spatial dimensions of the data to reduce computational complexity and increase translation invariance.
Normalization Layers (Batch Normalization):
These layers normalize the activations within a layer, which helps with training stability and convergence in deep networks.
The arrangement and composition of these layers, along with their associated parameters (weights and biases), are crucial aspects of neural network design. The goal is to construct a network architecture that can effectively learn and represent the patterns and relationships within the data, ultimately leading to successful performance on the target task, whether it's image classification, natural language processing, or any other machine learning problem.
Weights and Bias: Each connection between neurons has a weight associated with it, which determines the strength of the connection. A bias term is also associated with each neuron, which allows the neuron to learn an offset to make the model more flexible.
Activation Function: An activation function is applied to the weighted sum of inputs to introduce non-linearity into the model. Common activation functions include the sigmoid, ReLU (Rectified Linear Unit), and tanh (hyperbolic tangent). Activation functions enable neural networks to learn complex patterns and relationships in data.
Forward Propagation: During forward propagation, input data is passed through the network, and computations are performed layer by layer to generate predictions. Each neuron calculates its output based on the inputs, weights, bias, and activation function.
Loss Function: A loss function measures the difference between the predicted output and the actual target values. It quantifies how well the neural network is performing on a specific task. The goal during training is to minimize this loss function.
Backpropagation: Backpropagation is the process of updating the network's weights and biases based on the error calculated by the loss function. The gradients of the loss with respect to the weights and biases are computed, and these gradients are used to adjust the parameters in a way that reduces the loss.
Training: Training a neural network involves iteratively presenting a dataset to the network, calculating the loss, and using backpropagation to update the weights and biases. This process continues until the network's performance converges to an acceptable level.
Deep Learning: When a neural network has multiple hidden layers, it is referred to as a deep neural network. Deep learning involves training deep neural networks to automatically learn hierarchical features from the data, enabling the model to handle complex tasks.
Neural networks have demonstrated remarkable capabilities in various domains, including image recognition, natural language processing, speech recognition, and reinforcement learning. They are a crucial component of modern machine learning and have led to significant advances in artificial intelligence.
R is one of the best programming languages for applying neural nets.
library("neuralnet")Warning message:
package ‘neuralnet’ was built under R version 3.5.1
> library("neuralnet", lib.loc="~/R/win-library/3.5")
> library(neuralnet)
> library(MASS)
> data = Boston
> max_data <- apply(data, 2, max)
>
> data_scaled <- scale(data,center = min_data, scale = max_data - min_data)
Error in scale.default(data, center = min_data, scale = max_data - min_data) :
object 'min_data' not found
> index = sample(1:nrow(data),round(0.70*nrow(data)))
> train_data <- as.data.frame(data_scaled[index,])
Error in as.data.frame(data_scaled[index, ]) :
object 'data_scaled' not found
> test_data <- as.data.frame(data_scaled[-index,])
Error in as.data.frame(data_scaled[-index, ]) :
object 'data_scaled' not found
> n = names(data)
> net_data = neuralnet(f,data=train_data,hidden=10,linear.output=T)
Error in varify.variables(data, formula, startweights, learningrate.limit, :
object 'train_data' not found
>
> predict_net_test <- compute(net_data,test_data[,1:13])
Error in compute(net_data, test_data[, 1:13]) :
object 'net_data' not found
> str(data)
'data.frame': 506 obs. of 14 variables:
$ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
$ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
$ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
$ chas : int 0 0 0 0 0 0 0 0 0 0 ...
$ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
$ rm : num 6.58 6.42 7.18 7 7.15 ...
$ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
$ dis : num 4.09 4.97 4.97 6.06 6.06 ...
$ rad : int 1 2 2 3 3 3 5 5 5 5 ...
$ tax : num 296 242 242 222 222 222 311 311 311 311 ...
$ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
$ black : num 397 397 393 395 397 ...
$ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
$ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
> max_data <- apply(data, 2, max)
> min_data <- apply(data, 2, min)
> data_scaled <- scale(data,center = min_data, scale = max_data - min_data)
>
> index = sample(1:nrow(data),round(0.70*nrow(data)))
> train_data <- as.data.frame(data_scaled[index,])
> test_data <- as.data.frame(data_scaled[-index,])
>
> n = names(data)
> f = as.formula(paste("medv ~", paste(n[!n %in% "medv"], collapse = " + ")))
> net_data = neuralnet(f,data=train_data,hidden=10,linear.output=T)
> plot(net_data)
> predict_net_test <- compute(net_data,test_data[,1:13])
>
> predict_net_test_start <- predict_net_test$net.result*(max(data$medv)- min(data$me))
> test_start <- as.data.frame((test_data$medv)*(max(data$medv)-min(data$medv))+min(data$medv))
> MSE.net_data <- sum((predict_net_test_start - test_start)^2)/nrow(test_start)
> Regression_Model <- lm(medv~., data=data)
>
> summary(Regression_Model)
Call:
lm(formula = medv ~ ., data = data)
Residuals:
Min 1Q Median 3Q
-15.5944739 -2.7297159 -0.5180489 1.7770506
Max
26.1992710
Coefficients:
Estimate Std. Error t value
(Intercept) 36.4594883851 5.1034588106 7.14407
crim -0.1080113578 0.0328649942 -3.28652
zn 0.0464204584 0.0137274615 3.38158
indus 0.0205586264 0.0614956890 0.33431
chas 2.6867338193 0.8615797562 3.11838
nox -17.7666112283 3.8197437074 -4.65126
rm 3.8098652068 0.4179252538 9.11614
age 0.0006922246 0.0132097820 0.05240
dis -1.4755668456 0.1994547347 -7.39800
rad 0.3060494790 0.0663464403 4.61290
tax -0.0123345939 0.0037605364 -3.28001
ptratio -0.9527472317 0.1308267559 -7.28251
black 0.0093116833 0.0026859649 3.46679
lstat -0.5247583779 0.0507152782 -10.34715
Pr(>|t|)
(Intercept) 0.00000000000328344 ***
crim 0.00108681 **
zn 0.00077811 ***
indus 0.73828807
chas 0.00192503 **
nox 0.00000424564380765 ***
rm < 0.000000000000000222 ***
age 0.95822931
dis 0.00000000000060135 ***
rad 0.00000507052902269 ***
tax 0.00111164 **
ptratio 0.00000000000130884 ***
black 0.00057286 ***
lstat < 0.000000000000000222 ***
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 4.745298 on 492 degrees of freedom
Multiple R-squared: 0.7406427, Adjusted R-squared: 0.7337897
F-statistic: 108.0767 on 13 and 492 DF, p-value: < 0.00000000000000022204
> test <- data[-index,]
> predict_lm <- predict(Regression_Model,test)
> MSE.lm <- sum((predict_lm - test$medv)^2)/nrow(test)
> summary(Regression_Model)
Call:
lm(formula = medv ~ ., data = data)
Residuals:
Min 1Q Median 3Q
-15.5944739 -2.7297159 -0.5180489 1.7770506
Max
26.1992710
Coefficients:
Estimate Std. Error t value
(Intercept) 36.4594883851 5.1034588106 7.14407
crim -0.1080113578 0.0328649942 -3.28652
zn 0.0464204584 0.0137274615 3.38158
indus 0.0205586264 0.0614956890 0.33431
chas 2.6867338193 0.8615797562 3.11838
nox -17.7666112283 3.8197437074 -4.65126
rm 3.8098652068 0.4179252538 9.11614
age 0.0006922246 0.0132097820 0.05240
dis -1.4755668456 0.1994547347 -7.39800
rad 0.3060494790 0.0663464403 4.61290
tax -0.0123345939 0.0037605364 -3.28001
ptratio -0.9527472317 0.1308267559 -7.28251
black 0.0093116833 0.0026859649 3.46679
lstat -0.5247583779 0.0507152782 -10.34715
Pr(>|t|)
(Intercept) 0.00000000000328344 ***
crim 0.00108681 **
zn 0.00077811 ***
indus 0.73828807
chas 0.00192503 **
nox 0.00000424564380765 ***
rm < 0.000000000000000222 ***
age 0.95822931
dis 0.00000000000060135 ***
rad 0.00000507052902269 ***
tax 0.00111164 **
ptratio 0.00000000000130884 ***
black 0.00057286 ***
lstat < 0.000000000000000222 ***
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 4.745298 on 492 degrees of freedom
Multiple R-squared: 0.7406427, Adjusted R-squared: 0.7337897
F-statistic: 108.0767 on 13 and 492 DF, p-value: < 0.00000000000000022204
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