Distance-based outlier detection for high dimension, low sample size data

ABSTRACT

Despite the popularity of high dimension, low sample size data analysis, there has not been enough attention to the sample integrity issue, in particular, a possibility of outliers in the data. A new outlier detection procedure for data with much larger dimensionality than the sample size is presented. The proposed method is motivated by asymptotic properties of high-dimensional distance measures. Empirical studies suggest that high-dimensional outlier detection is more likely to suffer from a swamping effect rather than a masking effect, thus yields more false positives than false negatives. We compare the proposed approaches with existing methods using simulated data from various population settings. A real data example is presented with a consideration on the implication of found outliers.

KEYWORDS:

• Centroid distance
• HDLSS
• high-dimensional asymptotics
• maximal data piling distance
• multiple outliers

Disclosure statement

No potential conflict of interest was reported by the authors.