The problem of finding the pattern that deviates from other observation is termed as outlier. The detection of outlier is getting importance in research area nowadays due to the reason that the technique has been used in various mission critical applications such as military, health care, fault recovery, and many. The analysis of functional data and its depth function plays a crucial role in statistical model for detecting outlier. The depth values alone not enough for finding outliers, since all the low depth values not be an outlier. The main problem of using classical model is that it cannot cop up with the high dimensionality of the data This paper proposed a novel technique based on Reproducing Kernel Hilbert Space curve (RKHS) for detecting outliers in functional data. The proposed RKHS model is based on a special Hilbert space curve associated with a kernel so that it reproduces each function in the space to enhance the performance of data depth function. The proposed method uses distance weighted discrimination classification that avoids overfitting the model and provides better generalizability in high dimensions. The kernel depths perform better performances for detection of outlier in a number of artificial and real data sets.

Outlier identification and elimination are essential preprocessing steps for data analysis tasks such as clustering, classification, and regression. The accuracy of data analysis outcomes may be compromised if outliers are not adequately addressed. Detecting outliers is particularly challenging when they are characterized by unusual combinations of multiple attributes. Furthermore, the presence of outliers can impact various data processing activities, necessitating either the reduction of outlier influence or their complete removal. Outlier detection in multivariate data presents a complex process that becomes increasingly difficult when dealing with high-dimensional datasets. Consequently, this study focuses on the identification of such outliers in multivariate datasets using intelligent techniques. In the proposed approach, outliers are detected using an Improved Neural Network (INN), where the hidden neurons are tuned by a novel Synergistic Firefly-Grey Wolf Optimization (SF-GWO) algorithm. This algorithm combines the strengths of the Firefly Optimization (SFO) and Grey Wolf Optimization (GWO) techniques to maximize accuracy. The unique method results in enhanced classification model performance, reduced computation time, and increased classification accuracy. The proposed model has been evaluated and compared with well-established traditional techniques, demonstrating its effectiveness in addressing the challenges of outlier detection in multidimensional datasets.