# Review of Advances in Active Impulsive Noise Control with Focus on Adaptive Algorithms
## 4 Other Transformation Algorithms  
The MCC algorithm, formally known as the maximum correntropy criterion, aims to enhance performance by maximizing the probability of similarity in the local space between two sets of random variables. The core idea of this algorithm is to control the observation range of random variables through the adjustment of kernel width, thereby automatically excluding outliers. The MCC algorithm is essentially based on the mixed second-order norm of the error signal, typically employing a Gaussian kernel function. In the MCC algorithm, increasing the kernel width expands the observation space, making the algorithm gradually approach the FxLMS algorithm. Conversely, decreasing the kernel width narrows the observation space, thereby enhancing the MCC algorithm's resistance to impulsive noise. [PERSON] first introduced the concept of correntropy and theoretically analyzed the advantages of the MCC algorithm in handling impulsive noise [54]. The MCC algorithm exhibits \(l_{2}\) moment characteristics when two sets of analyzed signals are relatively similar, presents \(l_{1}\) moment properties when there is a slight difference in signals and shows \(l_{0}\) moment properties when the signal gap is larger. Therefore, it ensures the stability of the active noise control (ANC) system under impulsive noise interference. PRINCIPE utilized the MCC algorithm to identify and eliminate impulsive noise in system recognition under impulsive noise interference [55]. [PERSON] conducted a theoretical analysis, marking the first investigation into the long-term performance of the MCC algorithm and providing insights into its steady-state behavior [56]. [PERSON] proposed the GMCC algorithm, formally known as the generalized maximum correntropy criterion algorithm. They verified the stability of this equation under impulsive noise interference through theoretical derivation and simulation [57]. [PERSON] proposed a filtered-x recursive maximum correntropy algorithm with adaptive kernel width updates, demonstrating fast convergence and robustness against impulsive noise [58]. The results indicate that the algorithm exhibits a fast convergence rate in environments with a low pulse intensity (\(\alpha=1.7\)). By integrating the AP algorithm with other methods, [PERSON] proposed two novel adaptive approaches for addressing impulsive noise [59]. [PERSON] presented a multi-convex combination maximum correntropy adaptive algorithm. The synergy of the AP and GMCC algorithms can significantly improve the algorithm's effectiveness [60]. The algorithm achieves the best convergence performance when the parameter \(\alpha\) is set to 2. [PERSON] introduced a transformed kernel width MCC algorithm that operates as a fixed kernel width MCC algorithm when the error is small [61]. The algorithm proposed by [PERSON] adopts an improved conjugate gradient method to iteratively update filter coefficients, thereby enhancing the algorithm's performance [62]. [PERSON] introduced the kernel risk-sensitive loss (KRSL) algorithm, demonstrating from theoretical and simulation perspectives that this method achieves a fast convergence, high accuracy and robustness [63]. [PERSON] combined the minimum kernel risk-sensitive loss criterion with the \(p\)-norm method, proposing a new robust adaptive algorithm [64]. [PERSON] introduced the convex combination KRSL algorithm. Similar to the MCC algorithm, the performance of the KRSL algorithm is associated with the kernel width parameter [65]. Information-theoretic learning cost functions have the advantages of strong robustness and not requiring prior estimation of the impulsive noise characteristic parameter \(\alpha\). However, careful selection of the kernel width is necessary for optimal performance of this algorithm. In addition, [PERSON] combined the maximum skewness line criterion with the FxLMP algorithm, proposing a novel adaptive algorithm [66].