Practical Data Science using Python - Principal Component Analysis - Computations 2

The video tutorial explains the process of Principal Component Analysis (PCA) and its application in data analysis. It covers the eigen decomposition process, the role of eigenvectors and eigenvalues, and how they form principal components. The tutorial discusses diagonalization, covariance reduction, and the use of scree plots to determine the explained variance. It concludes with practical steps for applying PCA, including data standardization and recasting using eigenvectors.

What is the primary purpose of eigen decomposition in PCA?

• To increase the dimensionality of the data set

• To normalize the data set

• To split the covariance matrix into eigenvectors and eigenvalues

• To calculate the mean of the data set

How are eigenvectors used in PCA?

• As new data points

• As noise filters

• As new basis vectors for the transformed data set

• As labels for the data set

Which of the following best describes diagonalization in PCA?

• It eliminates all data variance

• It duplicates the original data set

• It transforms the data set to reduce feature covariance

• It increases the covariance between features

What happens to the covariance matrix after diagonalization?

• It becomes diagonal

• It becomes a random matrix

• It becomes a zero matrix

• It remains unchanged

What does a scree plot help determine in PCA?

• The number of principal components to retain

• The mean value of the data set

• The number of eigenvectors to discard

• The total number of data points

Which component in PCA captures the most variance?

• The component with the smallest eigenvalue

• The component with the largest eigenvalue

• The component with the average eigenvalue

• The component with the median eigenvalue

What is the role of eigenvalues in PCA?

• They determine the number of data points

• They rank the principal components by variance captured

• They eliminate noise from the data set

• They increase the dimensionality of the data set

Why is standardization important in the PCA process?

• To decrease the number of observations

• To ensure each feature contributes equally to the analysis

• To eliminate all data variance

• To increase the number of features

What is the final step in the PCA process before applying the Python demo?

• Eliminating all eigenvectors

• Increasing the number of dimensions

• Recasting the data set using selected principal components

• Calculating the mean of the data set

What is the significance of retaining a certain number of principal components?

• To reduce the number of observations

• To increase the complexity of the model

• To capture a sufficient amount of variance from the original data set

• To ensure all data points are used