Abstract
When I subjects answer questions regarding J variables K times, the data can be stored in a three-mode data set of size \(I \times J \times K\). Among the various component analysis approaches to summarize such data, Three-mode Principal Component Analysis (3MPCA) is often used. 3MPCA expresses a three-mode data set by means of A-, B-, and C-mode components and a core array, but this approach is not suitable for predicting data at unobserved time points. To handle this issue, the current study suggests a fixed orthonormal polynomial basis for the 3MPCA model. Briefly, we fix the C-mode component matrix with an orthonormal polynomial basis. More specifically, i) measurement time points, and ii) log transformation of the measurement time points were used as an orthonormal polynomial basis. The use of our proposed methods was demonstrated by applying them to a longitudinal data set collected from patients with depression.
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Acknowledgments
The second and last authors’ research was partially supported by JSPS Bilateral Program Grant Number JPJSBP 120219927, and the last author’s research was partially supported by JSPS KAKENHI Grant Number 20H04151.
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Monden, R., Nagai, I., Yanagihara, H. (2023). Implications of the Usage of Three-Mode Principal Component Analysis with a Fixed Polynomial Basis. In: Czarnowski, I., Howlett, R., Jain, L.C. (eds) Intelligent Decision Technologies. KESIDT 2023. Smart Innovation, Systems and Technologies, vol 352. Springer, Singapore. https://doi.org/10.1007/978-981-99-2969-6_19
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DOI: https://doi.org/10.1007/978-981-99-2969-6_19
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