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To solve the problem, we'll follow these steps: 1. Calculate the squared Euclidean distance between the input vector \( \mathbf{x} \) and each cluster weight vector \( \mathbf{w}_1 \) and \( \mathbf{w}_2 \). The squared Euclidean distance between two vectors \( \mathbf{x} = [x_1, x_2, ..., x_n] \) and \( \mathbf{w} = [w_1, w_2, ..., w_n] \) is given by: \[ D^2(\mathbf{x}, \mathbf{w}) = \sum_{i=1}^{n} (x_i - w_i)^2 \] 2. Find the winning cluster unit by determining which weight vector has the smallest squared Euclidean distance to the input vector \( \mathbf{x} \). 3. Update the weights for the winning unit using the learning rule: \[ \mathbf{w}_{\text{new}} = \mathbf{w}_{\text{old}} + \eta (\mathbf{x} - \mathbf{w}_{\text{old}}) ________ ________ ______ ____ ________ _________ _____ _____ ______.
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