MGMT90280 · Managerial Decision Analytics
Descriptive Data Mining: Cluster Analysis
Cluster analysis is the unsupervised heart of descriptive data mining in MGMT90280 Managerial Decision Analytics at the University of Melbourne: with no outcome variable to predict, the job is to group records so that members of a cluster are similar to each other and different from the rest. Everything rests on a single idea — a numeric measure of (dis)similarity: Euclidean distance for numeric data (after standardising), and the matching or Jaccard coefficients for binary data. From those distances you build groups with hierarchical linkages read off a dendrogram, or with k-means, and you classify a new record by its nearest centroid — the exact skills tested in the descriptive-data-mining slot of the 50% final exam.
What this chapter covers
- 016.1 Unsupervised learning: clustering with no outcome variable
- 026.2 Euclidean distance and why you must standardise (z-scores) first
- 036.3 Binary similarity: matching coefficient vs Jaccard's coefficient (and one-hot encoding)
- 046.4 Hierarchical linkages: single, complete, group-average, centroid
- 056.5 Reading and cutting a dendrogram (lines crossed = clusters)
- 066.6 The k-means loop: assign to nearest centroid, then recompute the mean
- 076.7 Nearest-centroid assignment for classifying a new record
- 086.8 Exam traps: standardising, the Jaccard denominator, and naming the linkage
Nearest-centroid assignment on two standardised features
- +1Rule & set-up. Standardise x on the same scale as the centroids, then assign it to the cluster whose centroid has the smallest Euclidean distance. Work with squared distances Σ(x−c)² and take the square root only of the winner.
- +1Distance to c₁: (0.5 − (−0.6))² + (−0.2 − 0.9)² = (1.1)² + (−1.1)² = 1.21 + 1.21 = 2.42.
- +1Distance to c₂: (0.5 − 0.8)² + (−0.2 − (−0.5))² = (−0.3)² + (0.3)² = 0.09 + 0.09 = 0.18.
- +1Compare. Squared distances are 2.42 (to c₁) and 0.18 (to c₂). The smaller is to c₂; its actual distance = √0.18 = 0.42, versus √2.42 = 1.56 for c₁.
- +1Decision. Assign the new customer to Cluster 2 — its centroid is the nearest by a wide margin, so the assignment is unambiguous. (Had x not been standardised on the training set's means and sds, this comparison would be meaningless.)
Key terms
- Euclidean distance
- The straight-line dissimilarity between two numeric records u and v over q variables: d(u,v) = √(Σ(u₁−v₁)² + … + (u_q−v_q)²). Smaller means more similar; 0 means identical. It is the default metric for k-means and nearest-centroid assignment.
- Standardisation (z-score)
- Rescaling each variable to z = (value − mean) / sd so it has mean 0 and sd 1. Euclidean distance is scale-sensitive, so a wide-range variable would otherwise dominate; standardising first lets every variable contribute fairly to the distance.
- Matching coefficient
- A similarity score for binary (0/1) records: (number of variables that match) ÷ (total number of variables). It counts both 1-1 and 0-0 agreements, so it treats a shared absence as similarity.
- Jaccard's coefficient
- A similarity score for binary records that counts only 1-1 matches: (variables matching on a 1) ÷ (total variables − variables matching on a 0). It ignores joint 0-0 positions — preferred when a shared absence is not real similarity, e.g. one-hot product baskets.
- Linkage (hierarchical)
- The rule for the distance between two clusters, used to decide which pair merges next. Single = closest pair (minimum); complete = farthest pair (maximum); group average = mean over all cross-cluster pairs; centroid = distance between the two cluster mean points.
- Dendrogram
- The tree diagram of an agglomerative hierarchical clustering. Leaf height where two branches join = the dissimilarity at which they merged. Cutting horizontally at a chosen height yields clusters; the number of vertical lines the cut crosses equals the number of clusters.
- k-means
- A clustering algorithm that fixes k and loops two steps: ASSIGN each record to its nearest centroid (Euclidean), then RECOMPUTE each centroid as the mean of its members, until assignments stop changing. It minimises within-cluster squared distance but only reaches a local optimum, so it is run from several starts.
- Nearest-centroid assignment
- The classification rule that gives a new record to the cluster k* = argmin_k d(x, c_k) — the cluster whose centroid is closest in Euclidean distance. In practice, compare the squared distances and pick the smallest.
Descriptive Data Mining: Cluster Analysis FAQ
When should I use Jaccard instead of the matching coefficient?
Use Jaccard when a joint absence (both records showing 0) is not genuine similarity. For one-hot-encoded categories or market-basket flags, almost every pair of records shares many 0s, so the matching coefficient inflates similarity through those joint absences; Jaccard removes the 0-0 positions from the denominator, giving the honest score. Use matching only when a shared 0 really is meaningful agreement.
How do I read the number of clusters off a dendrogram?
Cut the tree horizontally at a chosen dissimilarity height and count the vertical lines the cut crosses — that count is the number of clusters at that height. Cutting lower gives more, tighter clusters; cutting higher gives fewer, looser ones. Always state which linkage (single, complete, average or centroid) built the tree, because the same distances can give different merge heights and even different clusters.
Can AI help me with cluster analysis in MGMT90280?
Yes — Sia can explain it step by step. It will walk you through standardising your variables, computing Euclidean distances or matching/Jaccard coefficients, following the k-means assign-then-recompute loop, and reading a dendrogram, using its own worked practice numbers so you learn the method. It will not sit your assignment or exam or promise a grade — the timed Assignment 1 (Respondus LockDown Browser) forbids internet and generative AI, so use Sia only for study and revision beforehand and confirm the rules on the LMS.
Exam move
Carry the topics in the order a question unfolds. First decide the data type: numeric data means standardise every variable to a z-score, then use Euclidean distance; binary data means count matches and choose the matching coefficient (keeps 0-0) or Jaccard (drops 0-0), remembering to one-hot encode any multi-level category first. For grouping, practise agglomerative hierarchical clustering by hand on a small distance matrix — merge the closest pair, update distances by the stated linkage, and sketch the dendrogram with correct merge heights; for k-means, rehearse the assign-then-recompute loop and the nearest-centroid rule for a new record. Descriptive data mining is a 20-mark slot in the five-question final; at the bible-wide pace of about 1.2 minutes per mark that is roughly 24 minutes, so show the distance or coefficient arithmetic clearly and always finish with an explicit decision — which cluster, or how many clusters. Confirm the exact exam structure, date and permitted materials on the LMS.
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