Difference between revisions of "PCA Theory Examples Comment" - Rhea

Latest revision as of 15:35, 14 May 2014

This is the talk page for the sLecture notes on Basics & Examples of PCA. Please leave me a comment below if you have any questions, if you notice any errors or if you would like to discuss a topic further.

Review by Chiho Choi

• SUMMARY This slecture presents a mathematical concept of Principal Component Analysis (PCA) and its practical applications. In section 2, the author explains about basic linear algebra, such as eigenvectors, eigenvalues, and singular vector decomposition, which are required to understand how PCA works. Section 3 shows the way of projecting high dimensional data to lower dimensional space based on the concepts of section 2. Then, he/she demonstrates it using 2D data in Section 4.1 and 512x512 image in Section 4.2, respectively. Section 4.3 provides some limitations in such a case that PCA fails to reduce data dimensions as shown in Figure 8 – 13.

• STRENGTHS As the author mentioned, a generic PCA method is known as an efficient way to reduce dimensions for linearly distributed data. It is well-described with appropriate examples and reasonable figures. For this, the author experiments on both elliptical distributed data and nonlinear multimodal data. In addition, by applying PCA in image compression, it is easy to understand how to apply this method in practical applications.

• WEAKNESSES Even though the author provides a procedure of PCA in Section 3, it is confusing to understand how to reduce data dimensions using given formulas. Thus, it would be better if the author explains more details about it. Also, I recommend him/her to show a variant of PCA which properly handles nonlinear multimodal data, so that we can get a better sense of dimension reduction.

Review by Yanzhe Cui

• This slecture is skilled constructed and it's easy to follow. First, the author introduces some basic concepts about Eigenvectors, Eigenvalues, and Singular Vector Decomposition; Second, the author gives the basic procedure of PCA; Third, three examples are given to teach reader how to use PCA in practical projects. I have a question in Example 2: the author claimed that As the number of principal components increases, the projected image becomes visually close to the original image, but in practical, how to choose the number of principal components? Is there any computation trade off? I found a typo in the title of first part: Decompositoin, it should be Decomposition, please correct it. However, this is a very good and comprehensive slecture.

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