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Anomaly Detection

Anomaly Detection


By the end of this post, you would have the basic idea on below topics:

  • What are Anomalies/Outliers
  • Anomaly Detection
  • Types of Anomaly Detection Schemes
  • What are various Statistical Approaches such as 3-Sigma & Moving Average Based.


Set of data points that are considerably different than the remained of the data.


Credit Card Fraud Detection
Telecom Fraud Detection
Any Domain specific Fraud Detection etc.
Greatly used in Time Series Forecasting models for outlier removal


  • How many outliers are there in the data?
  • Method is unsupervised – Validation can be quite challenging
  • Finding needle in a haystack



There are considerably more “normal” observations than “abnormal” observations in the data.


General Steps:

1. Build a profile of the “normal” behavior
Profile can be patterns or summary statistics for the overall population.

2. Use the “normal” profile to detect anomalies
Anomalies are observations whose characteristics differ significantly from the normal profile.


  • Statistical based
  • Distance based
  • Model based


STATISTICAL BASED – Standard Deviation Technique

If we know that the distribution of values in the sample is Gaussian or Gaussian-like, we can use the standard deviation of the sample as a cut-off for identifying outliers.
The Gaussian distribution has the property that the standard deviation from the mean can be used to reliably summarize the percentage of values in the sample.

For example, within one standard deviation of the mean will cover 68% of the data.
So, if the mean is 50 and the standard deviation is 5, as in the test dataset above, then all data in the sample between 45 and 55 will account for about 68% of the data sample. We can cover more of the data sample if we expand the range as follows:

1 Standard Deviation from the Mean: 68%
2 Standard Deviations from the Mean: 95%
3 Standard Deviations from the Mean: 99.7%

A value that falls outside of 3 standard deviations is part of the distribution, but it is an unlikely or rare event at approximately 1 in 370 samples.
Three standard deviations from the mean is a common cut-off in practice for identifying outliers in a Gaussian or Gaussian-like distribution. For smaller samples of data, perhaps a value of 2 standard deviations (95%) can be used, and for larger samples, perhaps a value of 4 standard deviations (99.9%) can be used.

Let’s make this concrete with a worked example:

Sometimes, the data is standardized first (e.g. to a Z-score with zero mean and unit variance) so that the outlier detection can be performed using standard Z-score cut-off values. This is a convenience and is not required in general, and we will perform the calculations in the original scale of the data here to make things clear.
We can calculate the mean and standard deviation of a given sample, then calculate the cut-off for identifying outliers as more than 3 standard deviations from the mean.

The following example shows how the average (mean) and standard deviation looks like for sample metric (CPU Utilization) on a specific device, when there are three points of data for three Mondays at 2:00 AM.
Collect three data points:

Calculate the population mean = (76+4+6)/3 = 28.67
The standard deviation for this example is 33.48.

The following table depicts the hourly averages (mean) of rate data by day, the average (mean) of hourly averages and the population standard deviation of the hourly averages for the same day of the week, same hour:


Assume that NPM is polling CPU utilization data at a 15-minute interval.

The current CPU utilization is greater than/less than one standard deviation can be considered as minor anomalies.

MINOR anomaly = (current value > mean+ 1*SD) ||(current value < mean-1*SD) 

The current CPU utilization is greater than/less than two standard deviation can be considered as major anomalies.

MAJOR anomaly = (current value > mean+ 2*SD) ||(current value < mean-2*SD)

The current CPU utilization is greater than/less than two standard deviation can be considered as critical anomalies.

CRITICAL anomaly = (current value > mean+ 3*SD) ||(current value < mean-3*SD)

Thanks Sai Satish , for providing the concrete example on the Standard Deviation Technique.


I hope this document provides you the basic idea on Anomaly detection, we shall be covering the above statistical method in details (along with code) in another thread, keep exploring our posts, cheers!!

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