Local canonical correlation analysis (CCA)¹ using three spatially constrained models (non-negative constraint, sum constraint and max constraint) has been investigated previously to increase the accuracy of activation detection in fMRI data^2,3,4. However, better detection accuracy could be achieved by applying a more flexible constrained CCA model. This study introduces a family-constrained CCA method indexed by parameters $$$p$$$ and $$$\Psi$$$ (abbreviated as cCCA) which is solved efficiently using numerical optimization theory.Model: Let $$$Y = (Y_1,…,Y_m) \in R^m$$$ be a vector representing time courses (tc) of $$$m$$$ voxels ($$$m$$$=9 for 3 x 3 regions in a 2D slice), and $$$X = (X_1,…,X_n) \in R^n$$$ represents $$$n$$$ functions used to model the BOLD response. Using proposed cCCA, coefficients $$$\alpha \in R^m$$$ and $$$\beta \in R^n$$$ of $$$Y$$$ and $$$X$$$ are found by maximizing the canonical correlation coefficient $$$\rho(Y\alpha,X\beta) = \frac{cov(Y’\alpha,X’\beta)}{\sqrt{var(Y’\alpha)var(X’\beta)}}$$$, with spatial constraints $$$\alpha_1^p\geq\psi\sum_{k=2}^{m}\alpha_k^p$$$; $$$ \alpha_k>0, \forall k$$$; $$$\beta_j\neq 0, \forall j$$$; where $$$\alpha_1$$$ specifies the weight of the center voxel and $$$\alpha_n,n>1$$$ represent the weights of the other 8 neighboring voxels in a 3*3 voxel grid. The 3 known models^{2, 3, 4} are included in this new family model for fixed parameters $$$p$$$ and $$$\Psi$$$: (a) non-negative cCCA:$$$p=1, \Psi=0$$$; (b) sum constraint cCCA: $$$p=1, \Psi=1$$$ and (c) max constraint cCCA:$$$p = \infty, \Psi = 1$$$. In this new model, a larger $$$\Psi$$$ indicates a higher contribution of the center voxel, leading to the univariate solution when $$$\Psi = \infty$$$; whereas an increase of $$$p$$$ guarantees a higher contribution of neighboring voxels. The solution is obtained by converting cCCA into a constrained multivariate multiple regression problem and solving it with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) ⁵ optimization algorithm. Imaging: fMRI data (3.0T, TR/TE/FOV = 2s/30ms/22cm×22cm, 25 slices, coronal oblique, thickness/gap=4.0 mm/1.0 mm, resolution 96×96, 288 time frames) from six normal subjects (4-males/2-females, age: 30-36) each consisting of a resting-state dataset and a memory task dataset were analyzed. The memory task involves viewing faces paired with occupations and contained instruction, encoding, recognition and control (distraction) periods. Validation with Simulated data: Simulated data were generated on a 32*32 grid and activation pattern for each 3*3 local neighborhood with an active center following the empirical distribution of the real data by applying mass-univariate analysis for encoding v/s control contrast. To achieve a realistic noise distribution , wavelet-resampled resting-state tc were added to the true activated tc (p<1e-10 uncorrected) ⁶, with a noise fraction $$$f$$$ that was close to the real data ($$$f=0.65$$$ in our case). Both cCCA and conventional fMRI analysis techniques were applied to the simulated data and receiver operating characteristic (ROC) curve was used to evaluate the activation detection performance. Area under the ROC curve (AUC) was calculated within the range of false positive rate (FPR) from 0 to 0.1⁴. Validation with real data: cCCA with optimal $$$p$$$ and $$$\Psi$$$ was finally used to analyze the real data and compared with other conventional fMRI analysis techniques. Statistical Analysis: Wilk’s lambda statistics⁷ was used to determine whether the center voxel was active for a specific contrast $$$C$$$. Statistical threshold for significance was obtained by repeating the above analysis on the wavelet-resampled resting-state data 100 times until a stable null statistics was achieved. Fig.1 shows the simulated ground truth and activation patterns (p<0.01, uncorrected) using different methods. AUC calculated from the simulated data are listed in Table.1. Optimum combination of cCCA is obtained at $$$p=1, \Psi=2$$$, which increases the AUC by 10.29% as compared to the univariate analysis. Strong block artifacts indicating higher FPR are also observed in the unconstrained and non-negative constrained CCA (Fig.1). Whole brain activation t-map for real episodic memory data with contrast encoding v/s control is shown in Fig.2 (p<0.05, FWE). Significant activations are observed in hippocampus using our cCCA method with optimal parameters. A CPU time of less than two hours to analyze an entire brain dataset is achieved with the proposed cCCA method.In fMRI analysis, widely used mass-univariate approach usually detects fewer artifacts but also less activation. Conventional CCA is highly sensitive to activations but also produces a low specificity if no proper constraint is applied. The optimum combination $$$(p,\Psi)$$$ cCCA incorporates local information while keeping the center voxel to be dominant (with largest weight). Our method is able to detect activation more accurately while reaching nearly identical sensitivity as conventional CCA but with a higher specificity.A new family constrained local CCA model is introduced and efficiently solved. Higher detection accuracy for a fixed specificity is obtained with this cCCA model with both simulated and real fMRI data.