**1. Introduction**

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316 Advances in Bioengineering

Data science is an evolutionary step in interdisciplinary fields incorporating computer science, statistics, engineering, and mathematics. At its core, data science involves using automated and robust approaches to analyze massive amounts of data and to extract informative knowledge from them. Data science transforms traditional ways of analyzing problems and creates powerful new solutions. Diverse computational and analytical techniques contribute to data science. In this chapter, we review and also propose one type of data mining and pattern recognition strategy that has been under development in multiple disciplines (e.g. statistics and machine learning) with important applications ---- outlier or novelty detection [1-4].

In biomedical engineering, data science can make healthcare and medical imaging science not only more efficient but also more effective for better outcomes and earlier detection. Outlier and novelty detection in these domains plays an essential role, though it may be underappre‐ ciated and not well understood by many biomedical practitioners. From the healthcare point of view, an outlier probably reflects the need for heightened vigilance, if not full-fledged intervention. For example, an abnormally high glucose reading for a diabetic patient is an outlier which may require action. In high-dimensional medical imaging, developing automat‐ ed and robust outlier detection methods is a critical preprocessing step for any subsequent statistical analysis or medical research.

An exact definition of an outlier or novelty typically depends on hidden assumptions regard‐ ing the data structure and the associated detection method, though some definitions are general enough to cope with varieties of data and methods. For example, outliers can be considered as patterns in data that do not conform to a well-defined notion of "normal" behavior, or as observations in a data set which appear to be inconsistent with the remainder of that set of data. Figure 1 shows outliers in a 2-dimensional dataset. Since most of the

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

observations fall into clusters N1 and N2, they are two "normal" regions; while points in region O1 as well as points o2 and o3 are outliers (in red), due to their sufficiently far distance from the "normal" regions. Identifying observations inconsistent with the "normal" data, or detecting previously unobserved emergent or novel patterns is commonly referred to as *outlier detection* or *novelty detection* [5, 6]. The distinction between novel patterns and outliers is that the novel patterns are often incorporated into the "normal" model after being detected whereas outliers are typically removed or corrected. This chapter aims to consider both detection schemes and sometimes treat them interchangeably for some general purposes.

**Figure 1.** An example of outliers in a 2-dimensional dataset.

**Figure 2.** A 2-dimensional dataset with a multivariate outlier (lower right diamond in red).

Outlier and novelty detection methods can be divided into *univariate and multivariate* ap‐ proaches [7-10]. The early univariate methods typically assume a known data distribution, for example, independently and identically distributed (i.i.d). In addition, many tests for detecting univariate outliers further assume the distribution parameters and the outlier types are known. However, these assumptions may be violated in real applications. Moreover, in many situa‐ tions multivariate outliers can not be identified when each variable is examined independently. Multivariate analysis is usually required in these cases for precise outlier detection, which allows for interactions over different variables to be taken into account within the class of data. Figure 2 illustrates 2-dimensional data points, with the lower right observation (in red) a clear multivariate outlier but not a univariate one. When analyzing each measure separately with respect to the spread of values along the two dimensions, they are close to the center of the univariate distributions. Therefore, the relationships between the two variables shall be considered when testing for outliers, leading to multivariate methods that are the focus of this chapter.

observations fall into clusters N1 and N2, they are two "normal" regions; while points in region O1 as well as points o2 and o3 are outliers (in red), due to their sufficiently far distance from the "normal" regions. Identifying observations inconsistent with the "normal" data, or detecting previously unobserved emergent or novel patterns is commonly referred to as *outlier detection* or *novelty detection* [5, 6]. The distinction between novel patterns and outliers is that the novel patterns are often incorporated into the "normal" model after being detected whereas outliers are typically removed or corrected. This chapter aims to consider both detection

schemes and sometimes treat them interchangeably for some general purposes.

**Figure 1.** An example of outliers in a 2-dimensional dataset.

318 Advances in Bioengineering

**Figure 2.** A 2-dimensional dataset with a multivariate outlier (lower right diamond in red).

Outlier and novelty detection methods can be divided into *univariate and multivariate* ap‐ proaches [7-10]. The early univariate methods typically assume a known data distribution, for example, independently and identically distributed (i.i.d). In addition, many tests for detecting univariate outliers further assume the distribution parameters and the outlier types are known. However, these assumptions may be violated in real applications. Moreover, in many situa‐ tions multivariate outliers can not be identified when each variable is examined independently. Multivariate analysis is usually required in these cases for precise outlier detection, which

Another related topic is robust statistics for estimation that can handle outliers or at least is less sensitive to the influence of outliers. Robust statistics perform well with data drawn from a wide range of probability distributions, especially for distributions that are not normally distributed. Robust statistical methods have been developed for many common problems, such as estimating data properties including location and scatter or estimating model param‐ eters as in regression analysis [10, 11]. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a parametric distribution. A typical procedure or example of the former case is for multivariate estimation of location and covariance as well as for multivariate outlier detection. In this case, as a first step, the ap‐ proaches often try to search for a minimum number of observations with a certain degree of confidence being outlier-free. Based on this starting subset, location and covariance can be estimated robustly. In a second step, outliers can be identified through computing the observations' distances with respect to these initial estimates.

In this chapter, we review and also propose statistical and machine learning approaches for outlier and novelty detection, as well as robust methods that can handle outliers in data and imaging sciences. In particular, robust statistical techniques based on the Minimum Cova‐ riance Determinant (MCD) are introduced in Section 2, which include a classical and fast computation scheme of MCD and a few robust regression strategies. We present our newly developed multivariate Voronoi outlier detection (MVOD) method for time series data and some preliminary results in Section 3. This approach copes with outliers in a multivariate framework via designing and extracting effective attributes or features from the data; Voronoi diagrams allow for automatic configuration of the neighborhood relationship of the data points, facilitating the differentiation of outliers and non-outliers. Section 4 reviews varieties of machine learning methods for novelty detection, with a focus on probabilistic approaches. In Section 5, we present some existing and new technologies related to outliers and novelty in the area of imaging sciences. Section 6 provides concluding remarks of the chapter.
