Empirical Approach to Machine Learning by Plamen P. Angelov & Xiaowei Gu

Author:Plamen P. Angelov & Xiaowei Gu
Language: eng
Format: epub
ISBN: 9783030023843
Publisher: Springer International Publishing

6.3.2 Identifying Potential Anomalies

In the first stage of the AAD algorithm, the discrete multimodal typicality at is obtained using Eq. (4.​40). By extending to , one can obtain the multimodal typicality at each data sample (), denoted by .

The Chebyshev inequality [21] (see Eq. 4.​27) describes the probability of a particular data sample () to be standard deviations, away from the global mean . For the particular and most popular case of , the probability of to be more than away from is less than . In other words, on average, up to one out of nine data samples may be anomalous. Therefore, the AAD approach assumes that of the data samples within are potentially abnormal (the worst case). Nonetheless, it does not mean that they are actual anomalies.

The AAD approach, firstly, identifies the candidates for global anomalies as of the data samples within , which has the smallest , denoted by . Here, is a small integer corresponding to the in the “ sigma” rule based on the Chebyshev inequality. In this book, we use since the “3σ ” rule is one of the most popular approaches for identifying global anomalies in various applications [10, 36, 37]. However, in traditional approaches, n = 3 does directly influence detecting each anomaly. In contrast, in the AAD approach, this is simply the first stage of sub-selection of potential global anomalies. We also do not assume Gaussian/normal distribution, but consider it to be arbitrary.

Then, the AAD approach identifies the potential local anomalies, denoted by . As the next step, the AAD approach identifies the neighboring unique data samples around each unique data sample located in the hypersphere with as the center and as the radius by Condition 6.2:

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