Calculator Options
Understanding Normal and Anomalous Scatter Patterns
Anomaly scatter plots separate routine observations from unusual points. They reveal structure that summary statistics can hide. Clear separation helps teams inspect suspicious records before modeling.
Each point represents two measured features within the selected coordinate space. Nearby points often share similar behavior or operating conditions. Distant points may indicate errors, attacks, failures, or rare events.
This calculator supports several statistical scoring methods for different data shapes. Standard scores suit stable distributions with limited extreme contamination. Robust scores resist distortion from already unusual observations.
Core Scoring Logic
Euclidean distance measures each point from a chosen center. The mean center reflects every value in the dataset. The median center reduces sensitivity to isolated extreme coordinates.
Standard distance scoring subtracts average distance from each observed distance. The difference is divided by the distance standard deviation. Larger positive scores indicate increasingly unusual radial positions.
Modified scoring replaces the mean and deviation with robust alternatives. It uses median distance and median absolute deviation. This method performs better when outliers influence classical estimates.
Formula Used
The IQR method compares distances against the upper quartile boundary. Its threshold multiplies the interquartile range beyond that boundary. Values above the resulting fence receive anomalous classifications.
Mahalanobis distance considers feature variance and correlation together. It stretches detection boundaries along natural dataset directions. Correlated clusters therefore receive more suitable elliptical limits.
Scaling changes how both features influence calculated distances. Standard scaling equalizes spread using means and standard deviations. Robust scaling uses medians and interquartile ranges instead.
Z-score: zᵢ = max(0, (dᵢ − mean(d)) ÷ sd(d))
Modified score: mᵢ = max(0, 0.6745(dᵢ − median(d)) ÷ MAD(d))
IQR score: qᵢ = max(0, (dᵢ − Q3) ÷ IQR)
Mahalanobis: Mᵢ = √((vᵢ − μ)ᵀΣ⁻¹(vᵢ − μ))
How to Use This Calculator
Contamination mode estimates a threshold from the requested anomaly percentage. Fixed mode applies the exact threshold entered by users. Both modes support consistent experiments across repeated datasets.
Start by pasting one point per line into the dataset field. Provide X, Y, and an optional label. Then choose scoring, scaling, thresholding, and visual presentation options.
Submit the form and review the summary before interpreting colors. Inspect the strongest scores and any parsing warnings. Compare scatter structure with the score distribution chart.
Interpreting and Exporting Results
Anomalies are not automatically mistakes or harmful events. They are observations requiring context, verification, and careful review. Domain knowledge should guide every final operational decision.
Threshold tuning should reflect false alarm costs and missed anomaly risks in practice. Lower thresholds flag more points for investigation. Higher thresholds focus attention on only stronger deviations.
Exported results also support audits, comparisons, and downstream quality workflows. Saved scores preserve evidence behind each classification. Repeated analysis can expose drift across changing data batches.
Frequently Asked Questions
What makes a point anomalous?
A point becomes anomalous when its calculated score reaches the active threshold. The score reflects distance, spread, and selected scaling. Classification still requires practical context from the dataset owner.
Which detection method should I choose?
Modified Z-score works well with contaminated or skewed datasets. Classical Z-score suits cleaner, stable distributions. Mahalanobis distance helps when features show meaningful correlation.
Why should features be scaled?
Scaling prevents larger numeric ranges from dominating distance calculations. Standard scaling suits balanced distributions. Robust scaling better resists extreme values and heavy tails.
What does contamination mean?
Contamination estimates the expected percentage of unusual observations. The calculator converts that percentage into a score percentile. Actual anomaly rates may differ when scores contain ties.
Can labels contain spaces?
Yes, labels may contain spaces when commas or semicolons separate fields. Place coordinates first and the label last. Simple whitespace input supports one remaining label field.
What does covariance regularization do?
Regularization stabilizes covariance inversion for Mahalanobis scoring. It helps datasets with repeated or nearly aligned points. Excessive values can weaken genuine correlation structure.
Why can the boundary look elliptical?
Scaling transforms radial boundaries when displayed on original coordinates. Mahalanobis distance also creates correlation-aware ellipses. These shapes represent equivalent score limits across both axes.
Can I export the calculated results?
Yes, result buttons export detailed CSV and JSON files. Plot export creates a high-resolution chart image. Exports include coordinates, scores, labels, and classifications.
Should flagged points be deleted automatically?
No, unusual observations may represent valuable rare cases. Verify source quality and business meaning first. Always investigate flagged records before making automated operational decisions.