Noise vs Outliers — Differences and Answers

Definitions

• Noise is the random (or nonsystematic) component or distortion in the measured data — e.g., typing errors, random measurement error, or blurred/unclear attributes. It is the random part of a value that obscures the true pattern.
• Outliers are data objects (points, tuples) that behave very differently from the general behaviour or distribution of the rest of the data — they always deviate systematically in some interesting direction.

Aspect	Noise	Outliers
Source	random errors / random fluctuations	occasional exceptional data (can be legitimate interest or genuine anomaly)
Form	adds fuzziness to many points	a few points deviate strongly from the bulk
Data quality	generally removed/cleaned	can be kept (they may BE the target in fraud detection)
Relationship	noise can cause outliers	outliers are not necessarily noise

(i) Is noise ever interesting or desirable? Are outliers?

• Noise is usually not interesting or desirable — it is an undesirable error component; however some randomness/perturbation can be used in simulation or regularisation.
• Outliers ARE often interesting/desirable: in fraud detection, network intrusion, and medical anomaly detection an unusual tuple may be exactly what we are mining for.

(ii) Can noise objects be outliers?

Yes. Since noise is random error, in a small data set a noisy point can easily appear as an outlier — a tuple that deviates strongly from the rest — thereby becoming an outlier (noise-generated outlier).

(iii) Can noise make a typical value unusual or vice-versa?

Noise can easily change a typical attribute value into an unusual one (e.g., the measured age of a person typed 218 instead of 28 → the noisy value looks like an outlier). Conversely, an outlier can't become a "typical" point merely by adding noise; but noise can randomly mask a true-outlier so it appears normal/typical (e.g., extreme transaction value 4500 accidentally recorded as 450 masks it as uninteresting noise). So yes, noise can make a typical value look unusual and noise can also make an unusual value look typical.

  Tuples within same cluster are similar; different clusters are dissimilar.
  Clusters can be of arbitrary shape; outliers/noise are explicitly marked.
                                    |
              ┌─────────┴─────────┐
             ● ● ●        noise point

Summary

• Noise: random measurement error; usually removed/ignored.
• Outliers: genuinely deviant points; can be interesting and kept.
• Overlap: noise can produce outliers; outliers are not always noise; and noise can mask or create apparently "normal"/"unusual" values.