Estimation of common subspace order across multiple datasets: Application to multi-subject fMRI data

Detecting the dimension of the subspace correlated across multiple data sets in the sample poor regime

“…3 shows that the proposed technique works better than the techniques in [19], [20], [23] in estimating the model order d all for low values of SNR. It is also worth noting that the techniques in [19], [20] estimate only d all while the proposed method and [23] also detect the components correlated across subsets of the data sets along with their correlation structure. iii) Performance of the proposed method when the element-wise threshold is not met, for P = 5 data sets with d = d all = 2: We also investigate the performance of the proposed technique for determining the number of correlated components when some of the pairwise correlation coefficients do not meet the threshold required for Theorem 1.…”

“…The first component is correlated across all the data sets, the next three are correlated across two data sets only and the fifth component in each data set is uncorrelated with the other components. [20]. The methods in [16] and [17] require the assumption that if signal components are correlated across any data sets then they must be correlated across all data sets, and these methods fail to estimate the model order when this assumption is not met.…”

“…The methods in [16] and [17] require the assumption that if signal components are correlated across any data sets then they must be correlated across all data sets, and these methods fail to estimate the model order when this assumption is not met. This assumption is relaxed in [18] and generalized to arbitrary correlation structures in [19] and [20]. Alternatively, signal components correlated across a subset of the collection of data sets might also be of interest.…”

“…When the SNR is low, the proposed approach outperforms all competing techniques. ii) Evaluation of model-order selection with arbitrary correlation structure, for P = 4 data sets with d = 3, d all = 1: In this setting all the parameters are the same as in the previous scenario except that the first component [19] mCCA-KPD [20] mCCA-HT [23] Proposed of each data set is correlated with all other data sets but the other two components are only correlated across a subset of data sets. The second component is correlated across all except the first data set and the third component is correlated between data sets two and four.…”

“…Hence, d all = 0, d = 4 and d pq is the number of nonzero entries in the corresponding column. In both these examples, the techniques in[15]-[20] provide solutions for either d pq ρ Example with the correlation structure inFig. 1with three data sets each with five signal components.…”