Principal Component Analysis Considering Weights Based on Dissimilarity of Objects in High Dimensional Space

In this paper, a new hybridization of supervised principal component analysis (SPCA) and stochastic gradient descent techniques is proposed, and called as SGD-SPCA, for real large datasets that have a small number of samples in high dimensional space. SGD-SPCA is proposed to become an important tool that can be used to diagnose and treat cancer accurately. When we have large datasets that require many parameters, SGD-SPCA is an excellent method, and it can easily update the parameters when a new observation shows up. Two cancer datasets are used, the first is for Leukemia and the second is for small round blue cell tumors. Also, simulation datasets are used to compare principal component analysis (PCA), SPCA, and SGD-SPCA. The results show that SGD-SPCA is more efficient than other existing methods.

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The Uncertainty and Robustness of the Principal Component Analysis as a Tool for the Dimensionality Reduction

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.235.1 ◽

2015 ◽

Vol 235 ◽

pp. 1-8

Author(s):

Jacek Pietraszek ◽

Ewa Skrzypczak-Pietraszek

Keyword(s):

Experimental Data ◽

Principal Component Analysis ◽

Dimensionality Reduction ◽

Confidence Intervals ◽

Dimensional Space ◽

Experimental Studies ◽

Principal Component ◽

Component Analysis ◽

High Dimensional ◽

Data Points

Experimental studies very often lead to datasets with a large number of noted attributes (observed properties) and relatively small number of records (observed objects). The classic analysis cannot explain recorded attributes in the form of regression relationships due to lack of sufficient number of data points. One of method making available a filtering of unimportant attributes is an approach known as ‘dimensionality reduction’. Well-known example of such approach is principal component analysis (PCA) which transforms the data from the high-dimensional space to a space of fewer dimensions and gives heuristics to select least but necessary number of dimensions. Authors used such technique successfully in their previous investigations but a question arose: whether PCA is robust and stable? This paper tries to answer this question by re-sampling experimental data and observing empirical confidence intervals of parameters used to make decision in PCA heuristics.

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Using principal component analysis for neural network high-dimensional potential energy surface

The Journal of Chemical Physics ◽

10.1063/5.0009264 ◽

2020 ◽

Vol 152 (23) ◽

pp. 234103

Author(s):

Bastien Casier ◽

Stéphane Carniato ◽

Tsveta Miteva ◽

Nathalie Capron ◽

Nicolas Sisourat

Keyword(s):

Neural Network ◽

Principal Component Analysis ◽

Potential Energy ◽

Potential Energy Surface ◽

Energy Surface ◽

Principal Component ◽

Component Analysis ◽

High Dimensional

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High-Dimensional Data Dimension Reduction Based on KECA

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.303-306.1101 ◽

2013 ◽

Vol 303-306 ◽

pp. 1101-1104 ◽

Cited By ~ 2

Author(s):

Yong De Hu ◽

Jing Chang Pan ◽

Xin Tan

Keyword(s):

Principal Component Analysis ◽

Dimension Reduction ◽

High Dimensional Data ◽

Principal Component ◽

Good Method ◽

Component Analysis ◽

Renyi Entropy ◽

Rényi Entropy ◽

Kernel Principal Component Analysis ◽

High Dimensional

Kernel entropy component analysis (KECA) reveals the original data’s structure by kernel matrix. This structure is related to the Renyi entropy of the data. KECA maintains the invariance of the original data’s structure by keeping the data’s Renyi entropy unchanged. This paper described the original data by several components on the purpose of dimension reduction. Then the KECA was applied in celestial spectra reduction and was compared with Principal Component Analysis (PCA) and Kernel Principal Component Analysis (KPCA) by experiments. Experimental results show that the KECA is a good method in high-dimensional data reduction.

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