Data Science and Machine Learning (Theory and Projects) A to Z - Feature Extraction: PCA For Small Sample Size Problems(

The video tutorial explains the concept of Principal Component Analysis (PCA) with a focus on small sample size problems, where the number of dimensions exceeds the number of samples. It discusses the challenges of computing eigenvalues and eigenvectors in such cases and introduces dual PCA as a solution. The tutorial provides a step-by-step procedure for implementing dual PCA, which involves computing eigenvectors of a smaller matrix to indirectly obtain the desired eigenvectors. The video concludes with a brief mention of kernel PCA as a future topic.

What defines a small sample size problem in PCA?

• When the number of samples is zero

• When the dimensions are larger than the number of samples

• When the dimensions are equal to the number of samples

• When the number of samples is larger than the dimensions

In the UCI Machine Learning Repository example, what was the dimensionality of the feature space?

• 20,000

• 200,000

• 2,000

• 200

What is a major computational challenge of PCA with high dimensionality?

• Slow data processing

• Insufficient memory

• Intractable computation of eigenvalues and eigenvectors

• Lack of data

What is dual PCA primarily used for?

• Reducing the number of samples

• Handling small sample size problems

• Increasing the number of dimensions

• Improving data accuracy

In dual PCA, what is computed instead of the eigenvectors of the original matrix?

• Eigenvectors of a larger matrix

• Eigenvectors of a smaller matrix

• Eigenvectors of a non-existent matrix

• Eigenvectors of a random matrix

What is the relationship between the eigenvalues of the two matrices in dual PCA?

• They are different

• They are the same

• They are inversely proportional

• They are unrelated

What is the first step in the dual PCA procedure?

• Compute eigenvalues of the smaller matrix

• Compute eigenvalues of the original matrix

• Compute eigenvectors of the smaller matrix

• Compute eigenvectors of the original matrix

What is the final goal of the dual PCA process?

• To improve data accuracy

• To compute eigenvalues and eigenvectors of the original matrix

• To reduce the number of samples

• To increase the number of dimensions

What is the significance of the eigenvectors computed in dual PCA?

• They are used to compute eigenvalues

• They are used to reduce dimensions

• They are used to increase dimensions

• They are used to derive eigenvectors of the original matrix

What will be discussed in the next video following this tutorial?

• Data preprocessing

• Kernel PCA

• Advanced PCA techniques

• Linear regression