Iris_NN

A simple single-layer neural network in Excel using the Iris dataset. You can modify the learning rate and then iterate through epochs one at a time using the VBA buttons. To the right of the calculations is a visualisation of the neural net, and confusion matixes for the three outputs.

Neural Network Architecture

This neural network is designed to classify the Iris dataset into three classes: Iris-setosa, Iris-versicolor, and Iris-virginica. The network consists of a single input layer and a single output layer.

Input Layer

• Number of Neurons: 4
• Features:
  • Sepal length
  • Sepal width
  • Petal length
  • Petal width

Output Layer

• Number of Neurons: 3
• Classes:
  • Iris-setosa
  • Iris-versicolor
  • Iris-virginica
• Activation Function: Softmax

Weights and Biases

• Weights:

  • There are $4 \times 3 = 12$ weights, connecting each input feature to each output neuron.

  • Represented as a 4x3 matrix $W$:

    $W = \begin{bmatrix} W_{11} & W_{12} & W_{13} \\ W_{21} & W_{22} & W_{23} \\ W_{31} & W_{32} & W_{33} \\ W_{41} & W_{42} & W_{43} \end{bmatrix}$

• Biases:

  • Each output neuron has its own bias term, resulting in 3 bias terms in total.

  • Represented as a vector $b$:

    $b = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix}$

Forward Pass

During the forward pass, the network performs the following computations for each data point:

1. Linear Combination:

   • For each output neuron $j$, the linear combination of inputs is computed as:

     $z_j = \sum_{i=1}^{4} W_{ij} \cdot x_i + b_j$

     Where:

     • $W_{ij}$ is the weight connecting input $i$ to output $j$
     • $x_i$ is the input feature
     • $b_j$ is the bias for output $j$

2. Activation (Softmax):

   • The softmax function is applied to the linear combinations to obtain the output probabilities:

     $\text{softmax}(z_j) = \frac{e^{z_j}}{\sum_{k=1}^{3} e^{z_k}}$

     This ensures that the outputs are probabilities that sum to 1.

Summary of the Architecture

1. Input Layer:

   • 4 neurons (sepal length, sepal width, petal length, petal width)

2. Output Layer:

   • 3 neurons (Iris-setosa, Iris-versicolor, Iris-virginica)
   • Softmax activation function

3. Connections:

   • 12 weights (4 input features × 3 output classes)
   • 3 biases (one for each output neuron)