# Category Archives: math

Monitoring key performance indicators (KPIs), sales or any other product data means working within an ecosystem where very often you will see metrics correlating with each other. When a normal correlation between two metrics is broken, we have reason to suspect something strange is happening.

As an example, take a look at anomaly.io analytics during its early days (a long time ago). In the graphic above, the new users are shown in green and the returning users in red. Clearly, something strange happens in the middle of November. Let’s use some techniques to find out more!
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To determine the level of correlation between various metrics we often use the normalized cross-correlation formula.2
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To detect the correlation of time series we often use auto-correlation, cross-correlation or normalized cross-correlation. Let’s study these techniques to understand them better.
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Previously, we looked at using Twitter Breakout (EDM) to detect Anomalies. As with the popular E-Divisive, EDM detects mean shift and changes in distribution. Both algorithms work with seasonal time series, but perform even better without seasonality. Read More

What is seasonal adjustment? Why is it important, and when should we use it? How should it be done? In this article, we will answer these and many other questions related to seasonality in data.
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Time series decomposition works by splitting a time series into three components: seasonality, trends and random fluctiation. To show how this works, we will study the decompose( ) and STL( ) functions in the R language.
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It can be difficult to detect the underlying trend of a time series in the presence of anomalies, due to unwanted noise. Fortunately, there are techniques to take into account those anomalies, so you can work with this kind of time series. One of them is the moving median.

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.

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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