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IUPUI

1. Zhou, Dali. Massive data K-means clustering and bootstrapping via A-optimal Subsampling.

Degree: 2019, IUPUI

Purdue University West Lafayette (PUWL)

For massive data analysis, the computational bottlenecks exist in two ways. Firstly, the data could be too large that it is not easy to store and read. Secondly, the computation time could be too long. To tackle these problems, parallel computing algorithms like Divide-and-Conquer were proposed, while one of its drawbacks is that some correlations may be lost when the data is divided into chunks. Subsampling is another way to simultaneously solve the problems of the massive data analysis while taking correlation into consideration. The uniform sampling is simple and fast, but it is inefficient, see detailed discussions in Mahoney (2011) and Peng and Tan (2018). The bootstrap approach uses uniform sampling and is computing time in- tensive, which will be enormously challenged when data size is massive. k-means clustering is standard method in data analysis. This method does iterations to find centroids, which would encounter difficulty when data size is massive. In this thesis, we propose the approach of optimal subsampling for massive data bootstrapping and massive data k-means clustering. We seek the sampling distribution which minimize the trace of the variance co-variance matrix of the resulting subsampling estimators. This is referred to as A-optimal in the literature. We define the optimal sampling distribution by minimizing the sum of the component variances of the subsampling estimators. We show the subsampling k-means centroids consistently approximates the full data centroids, and prove the asymptotic normality using the empirical pro- cess theory. We perform extensive simulation to evaluate the numerical performance of the proposed optimal subsampling approach through the empirical MSE and the running times. We also applied the subsampling approach to real data. For massive data bootstrap, we conducted a large simulation study in the framework of the linear regression based on the A-optimal theory proposed by Peng and Tan (2018). We focus on the performance of confidence intervals computed from A-optimal sub- sampling, including coverage probabilities, interval lengths and running times. In both bootstrap and clustering we compared the A-optimal subsampling with uniform subsampling.

Advisors/Committee Members: Tan, Fei, Peng, Hanxiang, Boukai, Benzion, Sarkar, Jyotirmoy, Li, Peijun.

Subjects/Keywords: Kmeans; Bootstrap; Subsampling

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Zhou, D. (2019). Massive data K-means clustering and bootstrapping via A-optimal Subsampling. (Thesis). IUPUI. Retrieved from http://hdl.handle.net/1805/20024

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Zhou, Dali. “Massive data K-means clustering and bootstrapping via A-optimal Subsampling.” 2019. Thesis, IUPUI. Accessed August 24, 2019. http://hdl.handle.net/1805/20024.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Zhou, Dali. “Massive data K-means clustering and bootstrapping via A-optimal Subsampling.” 2019. Web. 24 Aug 2019.

Vancouver:

Zhou D. Massive data K-means clustering and bootstrapping via A-optimal Subsampling. [Internet] [Thesis]. IUPUI; 2019. [cited 2019 Aug 24]. Available from: http://hdl.handle.net/1805/20024.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zhou D. Massive data K-means clustering and bootstrapping via A-optimal Subsampling. [Thesis]. IUPUI; 2019. Available from: http://hdl.handle.net/1805/20024

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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