MLF End Term: 24 December 2023, Set ADD3 (September 2023 term)

Consider an encoder-decoder pair used for dimensionality reduction, where the encoder function is denoted as $f(x_1, x_2, x_3) = (x_1 + x_2 + x_3)/3$ and the decoder function is denoted as $g(u) = [u \;\; u^2 \;\; u]$.

Compute the reconstruction error $\left(R(f, g) = \dfrac{1}{n} \sum\limits_{i=1}^{n} \|X_i - g(f(X_i))\|^2\right)$ for the following dataset:

$X_1 = [1, 2, 0], \;\; X_2 = [-1, 1, 0], \;\; X_3 = [1, 2, 3]$

Enter the answer correct to two decimal places.