TALL ARRAY METHOD EFFICIENCY IN DATASET DIMENSIONALITY REDUCTION BY PRINCIPAL COMPONENT ANALYSIS
DOI:
https://doi.org/10.20535/kpisn.2025.2.331279Abstract
Background. Exploratory data analysis has been extensively growing since early 2000s. As of 2025, most real-practice datasets are classified as Big Data. The Big Data analytics workflow includes the data preprocessing step, which is the starting point of Big Data computational handling. At this step, the data are tried to get simplified as much as possible. The main paradigm is dimensionality reduction allowing to simplify and visualize high-dimensional datasets. Principal component analysis (PCA) is a linear dimensionality reduction technique. The PCA can be sped up by applying Tall Arrays, if the data are stored on disk. The Tall Array PCA (TAPCA) computes principal components incrementally using a divide-and-conquer strategy.
Objective. The objective is to determine when the TAPCA is factually efficient for dimensionality reduction. The two numeric types to be studied are double and single precision.
Methods. To achieve the said objective, random large datasets are generated as matrices of a specified numeric type. Then computational time of the ordinary MATLAB PCA applied to generated matrices is measured. Next, computational time of converting in-memory arrays (generated matrices) into tall arrays is measured. Computational time of the TAPCA applied to those generated matrices, to which the PCA is applied before, is measured as well.
Results. A comparative analysis of the averaged computational times reveals that computational time complexity of both the PCA and TAPCA is rather polynomial than strictly quadratic or cubic. There is a nearly-hyperbolic margin, which alternatively could be called the TAPCA efficiency threshold, in a plane of the number of dataset observations and the number of dataset features, by which the TAPCA and the ordinary PCA take approximately the same time to compute principal components.
Conclusions. In computing principal components for dimensionality reduction of large datasets stored on disk, the Tall Array method becomes efficient by two parallel processor workers if a dataset has at least 5 to 6 million entries. The Tall Array method is more efficient on datasets with double precision whose efficiency threshold is nearly 6 million entries, whereas the efficiency threshold for datasets with single precision is between 5 to 15.2 million entries
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