Statistical Methods for Anomaly Detection

Apply classical statistical techniques and machine learning algorithms to identify outliers and unusual patterns in network telemetry data.

Z-Score and Standard Deviation

The simplest statistical anomaly detection measures how far a data point deviates from the mean in terms of standard deviations. A Z-score above 3 (or below -3) typically indicates an anomaly:

z_score = (observed_value - mean) / standard_deviation

This works well for single metrics like bandwidth utilization or packet counts but struggles with multivariate data and non-Gaussian distributions common in network traffic.

Moving Average and EWMA

Exponentially Weighted Moving Average (EWMA) gives more weight to recent observations, making it responsive to trend changes while smoothing noise:

• Set a smoothing factor (alpha) between 0 and 1
• Higher alpha = more responsive to recent changes
• Compare current values against EWMA prediction bands
• Well-suited for time-series metrics like throughput and latency

Principal Component Analysis (PCA)

PCA reduces high-dimensional network data to its principal components. Anomalies appear as points with high reconstruction error when projected back to the original space:

1. Collect multivariate network features (bytes, packets, connections, protocols)
2. Fit PCA on normal traffic to learn the principal components
3. Project new data and measure reconstruction error
4. High reconstruction error indicates the data point doesn't fit normal patterns

Clustering Methods

Clustering groups similar network behaviors together. Points that don't belong to any cluster - or belong to very small clusters - are anomalies:

Isolation Forest

Isolation Forest is particularly effective for network anomaly detection. It isolates anomalies by randomly partitioning feature space - anomalies require fewer splits to isolate because they are rare and different:

• Highly efficient with high-dimensional data
• Handles large datasets well (sublinear time complexity)
• No assumptions about data distribution
• Returns anomaly scores for ranking severity