**Author details**

50], and outliers (or other assumption violations) in the time series would impact the model fitness. Robust regression can minimize the influence of these outliers. At the group level, after spatial normalization, a common strategy is to first save the regression parameters for each subject at each voxel and then perform a test on the parameter values. Robust regression used at this level can minimize the influence of outlying subjects. Wager et al. [51] used simulations to evaluate several robust techniques against ordinary least squares regression, and apply robust regression to second-level group analyses in three real fMRI datasets. Experimental results demonstrate that robust Iteratively Reweighted Least Squares (IRLS) at the second level is computationally efficient; it increases statistical power and decreases false positive rates when outliers are present. Without the presence of outliers, IRLS controls false positive rates at an appropriate level. In summary, IRLS shows significant advantages in group data analysis

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‐

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

This work is supported in part by a grant from the National Institute of Health, K25AG033725.

and gaining increasing interest in data and imaging sciences.

and in the hemodynamic response shape estimation for fMRI time series data.

**6. Conclusions**

332 Advances in Bioengineering

variate time series.

**Acknowledgements**

Michelle Yongmei Wang1,2,3,4\* and Chris E. Zwilling2

\*Address all correspondence to: ymw@illinois.edu

