StudyBrixFree worksheets, study guides and courses

Artificial intelligence · University

Clustering, distances and interpretation

Clustering groups examples according to a representation and similarity rule. The groups are not automatically true natural categories.

Make a worksheet

Prerequisites

Vectors and squared distances.

Study notes

Unsupervised task

Clustering groups examples according to a representation and similarity rule. The groups are not automatically true natural categories.

K-means

K-means alternates assignments to nearby centres with mean updates and seeks to reduce within-cluster squared distances.

Scaling

Feature units can dominate distance. Standardization choices can change clusters and should be justified.

Validation

Inspect stability, domain usefulness and sensitivity to settings. A visually separated plot is not by itself a universal quality certificate.

Worked examples

Points 2 and 6 belong to one one-dimensional cluster. Find their mean centre.

(2+6)/2=4.

4

Find squared Euclidean distance between (1,2) and (4,6).

(4−1)²+(6−2)²=9+16.

25

Check your understanding

  1. What does k specify in basic k-means?

    1. A learning rate for every algorithm
    2. The number of clusters
    3. The number of labels in every dataset
    4. The guaranteed accuracy

  2. Why can unit scaling change k-means results?

    1. Distances depend on feature magnitudes
    2. Units never affect distance
    3. Every feature is automatically causal
    4. Clusters ignore input coordinates

  3. For centre 3 and points 1 and 5, find total squared error.

  4. Why should a discovered cluster not immediately be given a sensitive personal label?

Answers and marking guidance

Answers and marking notes
  1. The number of clusters

    k is the chosen number of centres/clusters.

  2. Distances depend on feature magnitudes

    Large-scale features can dominate squared distances.

  3. 8

    (1−3)²+(5−3)²=4+4.

  4. The grouping may reflect representation choices, bias or noise rather than a justified personal attribute. Interpretation requires evidence and ethical care.

    Credit uncertainty and harm-aware interpretation.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

AI-assisted preview; independent educational review required. Level labels describe prerequisites, not accreditation or official curriculum alignment.