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 is the definition of a small sample size problem in the context of PCA?

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What is the relationship between the number of dimensions and the number of samples in a small sample size problem?

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Can you provide an example of a dataset that illustrates a small sample size problem?

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What challenges arise when computing the covariance matrix in PCA when D is much larger than N?

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What is dual PCA and how does it differ from traditional PCA?

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How can we compute eigenvalues and eigenvectors indirectly in the context of PCA for small sample sizes?

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What is the significance of computing eigenvectors of a smaller matrix instead of a larger one?

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Explain the process of obtaining eigenvectors from the matrix XC transpose X.

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What is the relationship between the eigenvalues of the matrices X transpose X and XC transpose?

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

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