MLT End Term: 24 December 2023, Set FDB1 (September 2023 term)

Common Data:

A team was given a dataset $X \in \mathbb{R}^{d \times n}$ where $d$ denotes the number of features and $n$ denotes the number of samples. They found that there are 10 samples in the dataset and each sample contains 100 features. Assume that the datapoints $x_4$ to $x_{10}$ are all linear combination of linearly independent data points $(x_1, x_2, x_3)$.

Based on the above data, answer the given subquestions.

Suppose the team applies linear PCA on the dataset and reconstructs the data points with zero error using k principal components (directions). For which value of k the reconstruction error would become zero?

Common Data:

A team was given a dataset $X \in \mathbb{R}^{d \times n}$ where $d$ denotes the number of features and $n$ denotes the number of samples. They found that there are 10 samples in the dataset and each sample contains 100 features. Assume that the datapoints $x_4$ to $x_{10}$ are all linear combination of linearly independent data points $(x_1, x_2, x_3)$.

Based on the above data, answer the given subquestions.