A series or set of algorithms that try to recognize the underlying relationship in a data set through a definite process that mimics the operation of the human brain is known as Neural Network. Hence, the neural networks could refer to the neurons of the human, either artificial or organic in nature. A neural network can easily adapt to the changing input to achieve or generate the best possible result by the network and does not need to redesign the output criteria.

#### Types of Neural Network

Neural Networks can be classified into multiple types based on their Layers and depth activation filters, Structure, Neurons used, Neuron density, data flow, and so on. The types of Neural Networks are as follows:

- Perceptron
- Multi-Layer Perceptron or Multi-Layer Neural Network
- Feed Forward Neural Networks
- Convolutional Neural Networks
- Radial Basis Function Neural Networks
- Recurrent Neural Networks
- Sequence to Sequence Model
- Modular Neural Network

#### Multi-Layer Neural Network

To be accurate a fully connected Multi-Layered Neural Network is known as Multi-Layer Perceptron. A Multi-Layered Neural Network consists of multiple layers of artificial neurons or nodes. Unlike Single-Layer Neural Network, in recent times most of the networks have Multi-Layered Neural Network. The following diagram is a visualization of a multi-layer neural network.

**Explanation:**

Here the nodes marked as “1” are known as **bias units**. The leftmost layer or Layer 1 is the **input layer**, the middle layer or Layer 2 is the **hidden layer** and the rightmost layer or Layer 3 is the **output layer**. It can say that the above diagram has **3 input units** (leaving the bias unit), **1 output unit, and 3 hidden units.**

A Multi-layered Neural Network is the typical example of the **Feed Forward Neural Network**. The number of neurons and the number of layers consists of the hyperparameters of Neural Networks which need tuning. In order to find ideal values for the hyperparameters, one must use some cross-validation techniques. Using the Back-Propagation technique, weight adjustment training is carried out.

#### Formula for Multi-Layered Neural Network

Suppose we have x_{n} inputs(x_{1}, x_{2}….x_{n}) and a bias unit. Let the weight applied be w_{1}, w_{2}…..w_{n.} Then find the summation and bias unit on performing dot product among inputs and weights as:

r = Σ^{m}_{i=1}w_{i}x_{i}+ bias

On feeding the r into activation function F(r) we find the output for the hidden layers. For the first hidden layer h^{1}, the neuron can be calculated as:

h_{1}^{1}= F(r)

For all the other hidden layers repeat the same procedure. Keep repeating the process until reach the last weight set.

#### Implementing Multi-Layered Neural Network in R

In R Language, install the ** neuralnet** package to work on the concepts of Neural Network. The

**package demands an all-numeric matrix or data frame. Control the hidden layers by mentioning the value against the hidden parameter of the**

`neuralnet`

**function which can be a vector for many hidden layers. Use the**

`neuralnet()`

**set.seed()**

function every time to generate random numbers.**Example:**

Use the **neuralnet** package in order to fit a linear model. Let us see steps to fit a Multi-Layered Neural network in R.

**Step 1:**The first step is to pick the dataset. Here in this example, let’s work on the**Boston**dataset of the**MASS**package. This dataset typically deals with the housing values in the fringes or suburbs of Boston. The goal is to find the medv or median values of the houses occupied by its owner by using all the other available continuous variables. Use thefunction to generate random numbers.`set.seed()`

`set.seed`

`(500)`

`library`

`(MASS)`

`data <- Boston`

*chevron_right**filter_none***Step 2:**Then**check for missing values or data points**in the dataset. If any, then fix the data points which are missing.`apply`

`(data, 2,`

`function`

`(x)`

`sum`

`(`

`is.na`

`(x)))`

*chevron_right**filter_none***Output:**crim zn indus chas nox rm age dis rad tax ptratio black lstat medv 0 0 0 0 0 0 0 0 0 0 0 0 0 0

**Step 3:**Since no data points are missing proceed towards**preparing the data set**. Now randomly split the data into two sets, Train set and Test set. On preparing the data, try to**fit the data on a linear regression model**and then**test**it on the test set.`index <-`

`sample`

`(1 :`

`nrow`

`(data),`

`round`

`(0.75 *`

`nrow`

`(data)))`

`train <- data[index, ]`

`test <- data[-index, ]`

`lm.fit <-`

`glm`

`(medv~., data = train)`

`summary`

`(lm.fit)`

`pr.lm <-`

`predict`

`(lm.fit, test)`

`MSE.lm <-`

`sum`

`((pr.lm - test$medv)^2) /`

`nrow`

`(test)`

*chevron_right**filter_none***Output:**Deviance Residuals: Min 1Q Median 3Q Max -14.9143 -2.8607 -0.5244 1.5242 25.0004 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 43.469681 6.099347 7.127 5.50e-12 *** crim -0.105439 0.057095 -1.847 0.065596 . zn 0.044347 0.015974 2.776 0.005782 ** indus 0.024034 0.071107 0.338 0.735556 chas 2.596028 1.089369 2.383 0.017679 * nox -22.336623 4.572254 -4.885 1.55e-06 *** rm 3.538957 0.472374 7.492 5.15e-13 *** age 0.016976 0.015088 1.125 0.261291 dis -1.570970 0.235280 -6.677 9.07e-11 *** rad 0.400502 0.085475 4.686 3.94e-06 *** tax -0.015165 0.004599 -3.297 0.001072 ** ptratio -1.147046 0.155702 -7.367 1.17e-12 *** black 0.010338 0.003077 3.360 0.000862 *** lstat -0.524957 0.056899 -9.226 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for gaussian family taken to be 23.26491) Null deviance: 33642 on 379 degrees of freedom Residual deviance: 8515 on 366 degrees of freedom AIC: 2290 Number of Fisher Scoring iterations: 2

**Step 4:**Now**normalize the data set**before training a Neural network. Hence, scaling and splitting the data. The

function returns a matrix which needs to be coerced in data frame.**scale()**`maxs <-`

`apply`

`(data, 2, max)`

`mins <-`

`apply`

`(data, 2, min)`

`scaled <-`

`as.data.frame`

`(`

`scale`

`(data,`

`center = mins,`

`scale = maxs - mins))`

`train_ <- scaled[index, ]`

`test_ <- scaled[-index, ]`

*chevron_right**filter_none***Step 5:**Now**fit the data into Neural network.**Use the**neuralnet**package.`library`

`(neuralnet)`

`n <-`

`names`

`(train_)`

`f <-`

`as.formula`

`(`

`paste`

`(`

`"medv ~"`

`,`

`paste`

`(n[!n %`

`in`

`%`

`"medv"`

`],`

`collapse =`

`" + "`

`)))`

`nn <-`

`neuralnet`

`(f,`

`data = train_,`

`hidden =`

`c`

`(4, 2),`

`linear.output = T)`

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Now our model is fitted to the Multi-Layered Neural netowrk. Now combine all the steps and also plot the neural network to visualize the output. Use the

function to do so.**plot()**

`# R program to illustrate ` `# Multi Layered Neural Networks ` ` ` `# Use the set.seed() function ` `# To generate random numbers ` `set.seed` `(500) ` ` ` `# Import required library ` `library` `(MASS) ` ` ` `# Working on the Boston dataset ` `data <- Boston ` `apply` `(data, 2, ` `function` `(x) ` `sum` `(` `is.na` `(x))) ` `index <- ` `sample` `(1 : ` `nrow` `(data), ` ` ` `round` `(0.75 * ` `nrow` `(data))) ` `train <- data[index, ] ` `test <- data[-index, ] ` `lm.fit <- ` `glm` `(medv~., data = train) ` `summary` `(lm.fit) ` `pr.lm <- ` `predict` `(lm.fit, test) ` `MSE.lm <- ` `sum` `((pr.lm - test$medv)^2) / ` `nrow` `(test) ` `maxs <- ` `apply` `(data, 2, max) ` `mins <- ` `apply` `(data, 2, min) ` `scaled <- ` `as.data.frame` `(` `scale` `(data, ` ` ` `center = mins, ` ` ` `scale = maxs - mins)) ` `train_ <- scaled[index, ] ` `test_ <- scaled[-index, ] ` ` ` `# Applying Neural network concepts ` `library` `(neuralnet) ` `n <- ` `names` `(train_) ` `f <- ` `as.formula` `(` `paste` `(` `"medv ~"` `, ` ` ` `paste` `(n[!n %` `in` `% ` `"medv"` `], ` ` ` `collapse = ` `" + "` `))) ` `nn <- ` `neuralnet` `(f, data = train_, ` ` ` `hidden = ` `c` `(4, 2), ` ` ` `linear.output = T) ` ` ` `# Plotting the graph ` `plot` `(nn) ` |

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**Output:**