Practical Data Science using Python - Principal Component Analysis - Computations 1

The video tutorial explains Principal Component Analysis (PCA), a technique used to reduce the dimensionality of data while retaining most of the variance. It covers the motivations for using PCA, such as simplifying complex models and improving visualization. The process involves standardizing data, calculating the covariance matrix, and deriving eigenvectors and eigenvalues. These eigenvectors form new axes that capture the most variance, allowing for data compression by selecting the most significant components.

What is one of the primary motivations for using PCA?

• To eliminate the need for data preprocessing

• To increase the number of features in a dataset

• To reduce the dimensionality of data

• To make data visualization more complex

What is the first step in the PCA process?

• Standardizing the data

• Calculating the covariance matrix

• Selecting principal components

• Finding eigenvectors

What does standardization of data involve?

• Scaling features to have a mean of zero and a standard deviation of one

• Setting all feature values to zero

• Normalizing data to a range of 0 to 1

• Removing all outliers from the dataset

What is a covariance matrix?

• A square matrix that shows the covariance between each pair of features

• A matrix that represents the variance of each feature

• A matrix that contains the means of all features

• A matrix that contains the sum of all feature values

What does a positive covariance value indicate?

• A direct relationship between two features

• A constant value for both features

• An inverse relationship between two features

• No relationship between two features

What is the purpose of eigen decomposition in PCA?

• To calculate the mean of the dataset

• To find the eigenvectors and eigenvalues of the covariance matrix

• To standardize the data

• To visualize the data in 3D

What do eigenvectors represent in PCA?

• The original features of the dataset

• The new basis vectors for the transformed data

• The mean values of the dataset

• The standard deviation of each feature

How are principal components selected in PCA?

• By selecting all available components

• Based on the largest eigenvalues

• Randomly from the dataset

• Based on the smallest eigenvalues

Why is it important to retain principal components with the highest eigenvalues?

• They capture the most variance from the original dataset

• They contain the least amount of noise

• They have the smallest data size

• They are easier to compute

What is the result of using PCA on a dataset with 200 features if only 15 principal components are retained?

• The dataset will be unchanged

• The dataset will have 15 features with increased variance

• The dataset will be reduced to 15 features that capture most of the variance

• The dataset will have 200 features with reduced variance