Our brains are really fast at recognizing patterns and forms: we can often find the seasonality of a signal in under a second. It is also possible do this with mathematics using the Fourier transform.

First, we will explain what a Fourier transform is. Next, we will find the seasonality of a website from its Google Analytics pageview report using the R language.

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Monitored metrics very often exhibit regular patterns. When the values are correlated with the time of the day, it’s easier to spot anomalies, but it’s harder when they do not. In some cases, it is possible to use machine learning to differentiate the usual patterns from the unusual ones.

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It is common to monitor the number of events that occur in a period of time. Unfortunately, this technique isn’t fast, and can fail to detect some anomalies. The alternative is to change the problem to studying the period of time between events.

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Instinctively we look at anomalies by examining the number of events during a fixed period of time. However, this method can’t achieve fast detection rates, and fails to detect some anomalies. The Poisson distribution turns the problem upside-down by looking at the period of time for a fixed number of events.

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The normal distribution is the holy grail of anomaly detection. Normally distributed metrics follow a set of probabilistic rules. Values that follow those rules are recognized as being “normal” or “usual”, while values that break them are seen as being unusual, indicating anomalies.
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