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Machine Learning Foundations, End Term
Consider an encoder-decoder pair used for dimensionality reduction, where the encoder function is denoted as and the decoder function is denoted as .
Compute the reconstruction error for the following dataset:
Enter the answer correct to two decimal places.
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. Figure from the original question paper Figure from the original question paper