Ns126:Calendar/NOTES/2015-4-17
5. Review Comments to the Author
Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)
Reviewer #1: In this paper, Dr. Xiong proposed to combine feature extraction and feature selection for image clustering analysis, and developed a 2-dim FPCA-based randomized feature selection algorithms. I have a few questions regarding the proposed randomized feature selection algorithms, and the following model comparison.
Q1: For randomized feature selection algorithms, determining the number of selected features (r) is important. It is set to be k+[k/ε]+1 in Page 15. Could we have more discussion on how it is derived?
Q2: Table 1 provides the comparison results for FPCA, Fourier expansion and SIFT descriptor by using standard k-means. However, this article proposed to combine FPCA with randomized sparse k-means. Could we have comparison results for these feature extraction methods by using randomized sparse k-means?
Q3: Table 2-4 provide the comparison results for standard k-means, sparse k-means and randomized sparse k-means. Randomized sparse k-means is applied to much fewer features and gets more accurate clustering results. However, in the framework feature extraction (or dimension reduction), we usually assume most features to be noises. Under this assumption, it would be natural to conclude that using fewer features could receive more accurate result. From this point of view, the comparisons in Table 2-4 are not quite fair. Could we compare these clustering methods by using same features to demonstrate that randomized sparse k-means has higher accuracy?
Minor revisions: Page 6, Line 6: "ß(t)" to "ß(s,t)" Page 6, Line 8, 11, 14, and 17: the domain of the first layer integration is S (not T). Page 7, Line 18: the notations n_{A} and n_{G} are confusing. Are they the sample sizes for X and Y. We can use n_{X} and n_{Y} instead. Page 8, Line 11: the notation ω is redundant, since the formula of Fourier series are not provided. Page 11, Line 16: "X_{i}X^{T}X" to "X_{i}X^{T}A". Page 12, Line 5: "the rank of the matrix A", "A" is missing. Page 16, Line 8, 10 and 11: "P_{i}" has already been used as points in Page 10. Page 8: "R" is used as Gaussian matrix. We should use other font to denote real line.
Reviewer #2: In this manuscript, the authors propose a model framework for feature selection and clustering in image data analysis. FPCA is generalized to a two-dimensional situation and combined into a randomized scheme for feature selection. K-means is then performed on the selected features for clustering analysis. While the manuscript is well-written with sufficient details of the model itself, the model performance needs to be further discussed to validate its value compared with existing methods.
I suggest the following changes to make the manuscript acceptable for publication:
Major comments: 1. The authors need to add some comparison between the generalized FPCA and existing methods for image data feature selection, such as GPCA, MPCA, etc, both in model performance and in computational cost. 2. The result of the randomized feature selection algorithm relies on the Gaussian matrix generated in the very beginning. The authors need to show the FPCA combined randomized scheme is stable in performance, both for feature selection and for clustering on selected features.
Minor comments: 1. The constraint of equation (2) is sensible because multiplying \beta by a constant will not change the selected features, not because "multiplying \beta by a constant will not change the maximizer of the variance". 2. In the mathematical deductions above equation (5), the third equal sign doesn't hold in general. Equation (5) is correct because the expression above should be 0 at the maximizer for arbitrary h(s,t), and h(s,t) can be replaced by that certain form. 3. In the result of feature selection using FPCA, 6 FPCs are sufficient for face image but 133 FPCs are selected for tumor cell image. The authors need to provide an explanation of the difference, e.g. how many pixels there are for the face image and tumor cell image.