LNN for Classification

February 15, 2026

Linear NN for Classification #

A Linear Neural Network (LNN) for classification uses no hidden layers.
It learns a linear decision boundary and outputs class probabilities, then converts them into predicted classes.

Neural-network view:

• Binary classification → logistic regression (single neuron + sigmoid)
• Multi-class classification → softmax regression (K output neurons + softmax)

flowchart LR
  D["Data<br/>X, y"] --> M["Linear model<br/>w, b"]
  M --> A["Activation<br/>Sigmoid / Softmax"]
  A --> L["Loss<br/>Cross-entropy"]
  L --> O["Optimiser<br/>Mini-batch GD / Adam"]
  O --> P["Updated parameters<br/>w, b"]
  P --> I["Inference<br/>Probabilities → class"]

  %% Pastel colour scheme
  style D fill:#E3F2FD,stroke:#1E88E5,stroke-width:1px
  style M fill:#E8F5E9,stroke:#43A047,stroke-width:1px
  style A fill:#FFF3E0,stroke:#FB8C00,stroke-width:1px
  style L fill:#FCE4EC,stroke:#D81B60,stroke-width:1px
  style O fill:#F3E5F5,stroke:#8E24AA,stroke-width:1px
  style P fill:#E0F7FA,stroke:#00838F,stroke-width:1px
  style I fill:#F1F8E9,stroke:#558B2F,stroke-width:1px

Classification #

Classification predicts a discrete class label.
Common settings:

Deep Feedforward Neural Networks (DFNN) for Classification

February 26, 2026

Deep Feedforward Neural Networks (DFNN) or Multi Layer Perceptrons (MLP) for Classification #

A Deep Feedforward Neural Network (DFNN), also called a Multi-Layer Perceptron (MLP), is a neural network with one or more hidden layers where information flows forward only (no recurrence).
For classification, DFNNs learn non-linear decision boundaries by combining hidden layers with non-linear activation functions.

Core idea:

• A single neuron can only learn linear boundaries.
• Adding hidden layers + non-linearity allows DFNNs to solve problems like XOR.

MLP as solution for XOR #

A single perceptron fails on XOR because XOR is not linearly separable.

Support Vector Machine

Support Vector Machine (SVM) #

A Support Vector Machine (SVM) is a supervised machine learning algorithm used for:

• Classification (most common)
• Regression (SVR – Support Vector Regression)

Find the decision boundary that separates classes with the maximum margin.

A Support Vector Machine is a supervised learning algorithm that finds an optimal hyperplane by maximising the margin between classes, using support vectors and kernel functions to handle non-linear data.