Multi-view spectral clustering has attracted considerable attention since it can explore common geometric structures from diverse views. Nevertheless, existing min-min framework-based models adopt internal minimization to find the view combination with the minimized within-cluster variance, which will lead to effectiveness loss since the real clusters often exhibit high within-cluster variance. To address this issue, we provide a novel scalable min-max multi-view spectral clustering (SMMSC) model to improve clustering performance. Besides, anchor graphs, rather than full sample graphs, are utilized to reduce the computational complexity of graph construction and singular value decomposition, thereby enhancing the applicability of SMMSC to large-scale applications. Then, we rewrite the min-max model as a minimized optimal value function, demonstrate its differentiability, and develop an efficient gradient descent-based algorithm to optimize it with linear computational complexity. Moreover, we demonstrate that the resultant solution of the proposed algorithm is the global optimum. Numerous experiments on different real-world datasets, including some large-scale datasets, demonstrate that SMMSC outperforms existing state-of-the-art multi-view clustering methods regarding clustering performance.

In this paper, a novel quaternion adaptive filtering algorithm is proposed for a unified processing of 3D and 4D data, called quaternion least mean kurtosis (QLMK) algorithm. Multi-dimensional signals exhibit a complex nonlinear relationship and couple among different components. Considering that quaternion has huge advantage in terms of the representation of 3D and 4D signal, quaternion algebra is employed to derive the quaternion least mean square (QLMS) algorithm for hypercomplex signal processes. However, QLMS originates from the least mean square (LMS) algorithm, which may result in performance degradation when the signal is non-Gaussian. Due to the desirable performance of the least mean kurtosis (LMK) algorithm in non-Gaussian situation, in the present work we extend the original LMK algorithm to quaternion domain to manage the 3D and 4D signal processes. The analysis shows that QLMK provides a solution that is responsive to dynamically changing environments. Simulations on prediction of 4D Saito's chaotic circuit and 3D Lorenz attractor confirm the desirable performance of the proposed method.

A bias-compensated normalized least mean absolute deviation (NLMAD) algorithm is developed for system identification under impulsive output measurement noise and noisy input environment, which takes the advantage of the NLMAD to resist impulsive output noises. Considering biased estimation caused by the noisy input, we employ an unbiasedness criterion to obtain a bias-compensated vector for NLMAD algorithm which can compensate the bias available. Simulation results show that the proposed algorithm can achieve better steady-state performance than the least mean absolute deviation (LAD) and NLMAD when the system meets the a-stable output measurement noise and noisy input case.

fMRI has been a popular way for encoding and decoding human visual cortex activity. A previous research reconstructed binary image using a sparse logistic regression (SLR) with fMRI activity patterns as its input. In this article, based on SLR, we propose a new sparse logistic regression with a tunable regularization parameter (SLR-T), which includes the SLR and maximum likelihood regression (MLR) as two special cases. By choosing a proper regularization parameter in SLR-T, it may yield a better performance than both SLR and MLR. An fMRI visual image reconstruction experiment is carried out to verify the performance of SLR-T.