Multiple Dataset Order Selection Algorithms
We present an algorithm, originally introduced in [2], for estimating the number of correlated components between two datasets when the dimensions of the datasets are large though number of samples is limited, the samplepoor regime, which is the case for multimodal fusion of medical imaging data [1]. This algorithm solves this problem by performing a principal component analysis (PCA) rankreduction preprocessing step before estimating the number of correlated components using the canonical correlation analysis (CCA). The proposed technique, principal component analysis and canonical correlation analysis (PCACCA), determines both the number of dimensions that should be retained through the PCA step and the number of correlated signals found using CCA using reducedrank versions of the classical BartlettLawley hypothesis test [3], [4] and the minimum description length informationtheoretic criterion, respectively. Though motivated by the case where the number of samples is much smaller than the dimension of the datasets, PCACCA also shows high performance in the samplerich regime as well.

Principal Component Analysis and Canonical Correlation Analysis (PCACCA) (PCACCA) [1], [2]
PCACCA
PCACCA is based upon a sequence of hypothesis tests, similar to the classical BartlettLawley test [3], [4].
References:
[1] Y. LevinSchwartz. Y. Song, P. J. Schreier, V. D. Calhoun, T. Adali, "Samplepoor estimation of order and correlated signal subspace with application to fusion of medical imaging data," NeuroImage, vol. 134, pp. 486493, 2016.
[2] Y. Song, P. J. Schreier, D. Ramirez and T. Hasija, "Canonical correlation analysis of highdimensional data with very small sample support," Signal Processing, vol. 128, pp. 449458, 2016.
[3] M. S. Bartlett, "The statistical significance of canonical correlations," Biometrika, vol. 32, no. 1, pp. 2937, 1941.
[4] D. N. Lawley, "Tests of significance in canonical analysis," Biometrika, vol. 32, no. 1, pp. 5966, 1959.