Answer: (iii) Neural Networks

Backpropagation is the standard learning (training) algorithm for multilayer feed-forward neural networks. It works in two phases:

1. Forward pass — the input is propagated layer by layer through the network, and the output at the output layer is computed.
2. Backward pass — the error (difference between actual output and expected output) is propagated backwards through the network to update each weight using the gradient descent rule:

$$w_{ij} \leftarrow w_{ij} + \eta\, \delta_j \, x_{ij}$$

where $\eta$ is the learning rate, $\delta_j$ is the error term of node $j$, and $x_{ij}$ is the input arriving along weight $w_{ij}$.

Why the others are wrong:

• (i) Decision Trees use attribute-selection measures such as information gain / Gini index, not backpropagation.
• (ii) Association Rules are found using algorithms like Apriori or FP-growth.
• (iv) Hierarchical Clustering uses distance-based agglomeration (AGNES/DIANA), not backpropagation.

Hence backpropagation is commonly used in Neural Networks.