Neural networks, a key concept in the field of data analysis, are a type of artificial intelligence model inspired by the human brain. These networks are designed to recognize patterns and interpret data through machine perception, labeling or clustering raw input. The patterns they recognize are numerical, contained in vectors, into which all real-world data, be it images, sound, text or time series, must be translated.

The term “neural network” is derived from its design as a representation of a human brain’s biological neural network. However, modern neural networks are a model of understanding rather than a model of the brain’s functionality. They are a means of doing machine learning, in which a computer learns to perform some task by analyzing training examples. Usually, the task involves making accurate predictions or decisions without being explicitly programmed to perform the task.

## Components of Neural Networks

Neural networks are made up of layers of nodes, or “neurons”, each of which performs a simple computation on the data. These computations are organized into a hierarchy, with the output of one layer serving as the input for the next. This hierarchical structure allows neural networks to process complex data in a way that simpler algorithms cannot.

The basic building block of a neural network is the neuron, often called a node or unit. It receives input from some other nodes, or from an external source and computes an output. Each input has an associated weight (w), which is assigned on the basis of its relative importance to other inputs. The node applies a function f (defined as the activation function) to the weighted sum of its inputs.

### Input Layer

The input layer is the very beginning of the workflow for the artificial neural network. It is composed of artificial input neurons, and brings the initial data into the system for further processing by subsequent layers of artificial neurons. The input layer is the very first layer that receives input from the user for further processing.

Each artificial neuron in the input layer is associated with one individual predictor variable or feature in your dataset. It’s the job of the input layer to distribute the data to the artificial neurons in the next layer. It’s important to note that the input layer does not perform any computations on the data. It only distributes the data to the next layer.

### Hidden Layer

The hidden layers are located between the input layer and the output layer. These layers perform computations and then transfer the weight (signals or information) from the input layer to the following layer. It’s called a “hidden” layer because it’s not visible as an input or output to the user and works behind the scenes.

The number of hidden layers and the number of neurons in each hidden layer can vary and are hyperparameters that can be set. The more hidden layers or neurons in each layer, the more complex patterns the network can recognize. However, too many layers or neurons can lead to overfitting, where the network performs well on training data but poorly on new, unseen data.

### Output Layer

The output layer is the final layer in the neural network. It receives inputs from the last hidden layer and transforms them into a form that is usable by the outside world. It’s the responsibility of the output layer to output a vector of values that is in a format that is suitable for the type of problem that you’re trying to address.

For example, for a regression problem, the output layer would have one neuron and output a single continuous numeric value. For a binary classification problem, the output layer would have one neuron and output a value between 0 and 1 to represent a probability. For a multi-class classification problem, the output layer would have one neuron per class and output a probability distribution over the classes.

## Activation Functions

Activation functions are mathematical equations that determine the output of a neural network. The function is attached to each neuron in the network, and determines whether it should be activated (“fired”) or not, based on whether each neuron’s input is relevant for the model’s prediction. Activation functions also help normalize the output of each neuron to a range between 1 and 0 or between -1 and 1.

There are several types of activation functions, each with its own advantages and disadvantages. The choice of activation function can significantly affect the performance of a neural network. Some of the most commonly used activation functions include the sigmoid function, the hyperbolic tangent function, and the rectified linear unit (ReLU) function.

### Sigmoid Function

The sigmoid function is a type of activation function that is traditionally very popular with neural networks. The sigmoid function is a smooth, continuously differentiable function that has a fixed output range between 0 and 1. It is especially useful in the output layer of a binary classification network, where we need an answer in terms of probabilities.

However, the sigmoid function has a couple of major drawbacks. First, it suffers from the “vanishing gradient” problem, where the gradients are very close to zero and the network refuses to learn further or is drastically slow. Second, its output isn’t zero-centered. It makes the gradient updates go too far in different directions. 0 < output < 1, and thus it’s not symmetric around zero, which makes the learning harder.

### Hyperbolic Tangent Function

The hyperbolic tangent function, or tanh for short, is another type of activation function that is also smooth and differentiable. The output of the hyperbolic tangent function is zero-centered because its range lies between -1 and 1, hence optimization is easier in this method hence in practice it is always preferred over the sigmoid function.

However, the tanh function also has the vanishing gradient problem just like the sigmoid function. Because of this, the use of both the sigmoid and tanh functions in hidden layers of a neural network is less common now, and they are primarily used for binary classification problems in the output layer.

### Rectified Linear Unit (ReLU) Function

The Rectified Linear Unit, or ReLU, is the most commonly used activation function in the field of deep learning. We use ReLU activation function because it does not activate all the neurons at the same time. This means that at a time only a few neurons are activated making the network sparse making it efficient and easy for computation.

The function returns 0 if it receives any negative input, but for any positive value x it returns that value back. So it can be written as f(x)=max(0,x). Even though it looks like it has a sharp corner, it works well in practice and has the advantage of being computationally efficient. Despite its name and appearance, it’s not linear and provides the same benefits that non-linear activation functions provide.

## Training Neural Networks

Training a neural network involves adjusting its weights and biases based on the error of its predictions. This is done using a process called backpropagation and an optimization technique, such as gradient descent. The goal of training is to minimize the difference between the network’s prediction and the actual output in the training data.

During training, the input is passed through the network, generating an output. This output is compared with the desired output, and the error is calculated. This error is then propagated back through the network, adjusting the weights and biases along the way. This process is repeated multiple times, with the goal of minimizing the error.

### Backpropagation

Backpropagation is a method used to train neural networks by calculating the gradient of the loss function. This gradient is then used to update the weights and biases in the network. Backpropagation works by using the chain rule from calculus to iteratively compute gradients at each layer.

The backpropagation algorithm starts at the end of the network. It calculates the derivative of the loss function with respect to the output of the last layer (the prediction). Then it steps backwards through the network, one layer at a time, calculating the derivative of the loss with respect to the output of each layer. These derivatives are then used to update the weights and biases in the network.

### Gradient Descent

Gradient descent is an optimization algorithm that’s used when training a machine learning model. It’s based on a convex function and tweaks its parameters iteratively to minimize a given function to its local minimum.

Gradient descent is best used when the parameters cannot be calculated analytically (e.g. using linear algebra) and must be searched for by an optimization algorithm. The algorithm is iterative, meaning that we need to get the results multiple times to get the most optimal result. The learning rate or step size determines how fast or slow we will move towards the optimal weights. If the step size is very small, we will move slowly towards the optimal weights, but if it is big we will have quicker computations.

## Applications of Neural Networks

Neural networks have a wide range of applications in many different areas. They are used in business for customer research, forecasting and investment modeling. In healthcare, they are used for medical diagnosis and research. In technology, they are used for pattern recognition, speech recognition, and computer vision. In finance, they are used for credit scoring and algorithmic trading.

One of the key advantages of neural networks is their ability to process large amounts of data and identify patterns and trends. This makes them particularly useful in the field of data analysis, where they can be used to make predictions and inform decision making. Neural networks are also highly adaptable and can be trained to perform a wide range of tasks, making them a versatile tool for data analysts.