How does neural network handle non-linear data better than logistic regression?

It is better to talk about linear and nonlinear separability as a notion in this context. The classes that can be separated by a hyperplane decision boundary are linearly separable, and not linearly separable otherwise. Neural networks learn to map the data into a space, where the classes are easily separable. While, logistic regression is a linear classifier and perfectly separates only linearly separable classes. Non-linear data could imply elements not associated with class separation, suggesting different sources of non-linearity. Complex dynamics, temporal delays, non-linear associations of features may all generate non-linear data. Yet, depending on the classes, the decision boundary could still end up linear.

Logistic regression assumes a linear relationship between the input features and the target variable. This means it may not perform that well when the relationship between the feature and outcomes is non-linear (This is where the neural network comes in). Logistic regression is not suited for problems where the decision boundary between classes is complex. More complex algorithms like Decision Trees, Random Forest and ANN are more appropriate. Also, standard logistic regression is designed for binary classification problems, can be extended to multi-class by using techniques like softmax, further adding complexity.

This activation function introduces nonlinearity into the output of a neuron. The purpose of an activation function is to map the output of a neuron to a form that can be understood and processed effectively by the next layer. This mapping often involves limiting the neuron’s output to a specific range of values. Without activation functions, even a deep neural network would be equivalent to a single-layer linear model because the composition of linear functions is still linear. The types of activation functions include, but are not limited to, sigmoid, hyperbolic tangent (tanh), rectified linear unit (ReLU), leaky ReLU, parametric ReLU (PReLU), exponential linear units (ELUs), softmax, and Swish.

1. **Layered Architecture**: Neural networks utilize multiple layers of neurons that enable them to model complex patterns through hierarchical feature extraction, unlike logistic regression which is limited to linear decision boundaries. 2. **Activation Functions**: Neural networks employ non-linear activation functions (like ReLU, sigmoid, tanh) at each neuron, allowing them to capture non-linear relationships in data, a capability logistic regression lacks due to its linear nature. 3. **Flexibility and Depth**: With the ability to adjust the number of layers and neurons, neural networks can be tailored to the complexity of the data, offering superior flexibility for modeling non-linearities compared to the single-layered regression.