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Visualizing singular value decomposition

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Abstract Singular value decomposition/principal component analysis method is a central tool in multivariate analysis and functional data analysis. In this article, a list of visualization tools that are useful in revealing structure within sample datasets is investigated. An Internet traffic dataset is used to illustrate the usefulness of these methods. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification Algorithms and Computational Methods > Computer Graphics Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization
The left panel shows the biplot for the Internet traffic data, and the right panel shows the linear‐angle plot for the time‐of‐day effects. The biplot shows that the dates form two groups, which correspond to weekday and weekend. In addition, a special date, June 29, is between the two clusters. The time‐within‐a‐day is overplotted in the biplot. The linear‐angle plot on the right highlight the clusters of the time within‐a‐day. The time from midnight to morning and then to evening are coded in rainbow color. It clearly highlights night and day effect, and the one hour 7–8 on the morning are between the two clusters.
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Bagplots and boxplots for the Internet traffic data: (a) the bivariate bagplot for the first two PCs, (b) the functional bagplot based on the first two PCs, showing the major group of functions, and some outlying daily shapes, (c) the bivariate boxplot for the first two PCs, showing two high density regions and (d) the functional boxplot, showing the outlying daily shapes.
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Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization
Algorithms and Computational Methods > Computer Graphics
Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification

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