Question 1

Figure from the original question paper **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. Figure from the original question paper