**6. Conclusions**

Outlier and novelty detection is a primary step in many data mining and analysis applications, including healthcare and medical research. In this chapter, statistical and machine learning methods for outlier and novelty detection, and robust approaches for handling outliers in data and imaging sciences were introduced and reviewed. Particularly, we also presented our new method for outlier detection in time series data based on the Voronoi diagram (i.e. MVOD). There are several key advantages of our method. First, it copes with outliers in a multivariate framework by accounting for multivariate structure in the data. Second, it is flexible in extracting valid features for differentiating outliers from non-outliers, in the sense that we have the option of using or not using a parametric model. Lastly, Voronoi diagrams capture the geometric relationship embedded in the data points. Initial experimental results show that our MVOD method can lead to accurate, sensitive, and robust identification of outliers in multi‐ variate time series.

It is often difficult to reach a precise definition of outlier or novelty, and suggesting an optimal approach for outlier or novelty detection is even more challenging. The variety of practical and theoretical considerations arising in real-world datasets lead to the variety of techniques utilized [52]. Therefore, there is no single universally applicable detection method due to the large variety of considerations, which could include the application domain, the type of data such as dimension, and the availability of training data, etc. Based on the application and the nature of the associated data, developing suitable computational methods that can robustly and efficiently extract useful quantitative information from big data is still a current challenge and gaining increasing interest in data and imaging sciences.
