What does second factor mean in Parallel Factor Analysis?

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In Parallel Factor Analysis (PARAFAC), the second factor represents an additional layer of decomposition that helps to capture more complex relationships within multi-dimensional data arrays. The first factor typically identifies the primary structure, while the second factor allows for the exploration of secondary patterns or interactions. Understanding the second factor is crucial for interpreting the nuances of the data and enhancing the analysis. This method aids in focusing on specific features of interest, leading to clearer results. Overall, the second factor enriches the insights gained from PARAFAC.
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There is a first factor and second factor in PARAFAC. What does second factor mean?

background:

Parallel Factor Analysis (PARAFAC; Hitchcock, 1927; Carrol and Chang, 1970; Harshman, 1970) is a method to decompose multi-dimensional arrays in order to focus on the features of interest, and provides a distinct illustration of the results.
 

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