On a silhouette plot the average is 0.42 but one cluster's bars are negative and another's are all short — what does that tell you?

### What the plot actually draws A silhouette plot has one horizontal bar per point. Bars are grouped by cluster and sorted within each group, so each cluster appears as a wedge. Two things are readable at a glance: the **length** of the bars, which is each point's silhouette score, and the **height** of each block, which is how many points that cluster contains. A single average destroys both. Take a five-cluster partition of e-commerce session features — session length, pages viewed, cart events, time since last visit and so on. The overall silhouette is 0.42, which reads as acceptable. The plot tells a different story. ### The cluster with negative bars Negative silhouette means the cohesion term exceeded the separation term: on average these points are nearer another cluster's members than their own. A whole block running negative is a structural statement, not a handful of odd rows. The two usual causes: - **Two groups overlap.** The cluster occupies the same region as a neighbour and the boundary between them is arbitrary. Whatever produced the split is drawing a line through one continuous mass of sessions. - **One real group was cut in two.** Half the sessions ended up on each side of a division that does not exist in the data, so each half is closer to the other half than to itself. The useful next step is that silhouette already names the culprit: the separation term is defined by the *nearest* other cluster, so you can record, per negative point, which cluster that was. If four fifths of the negative points in cluster 4 point at cluster 2, you have located a specific overlapping pair rather than a vague quality problem. Size changes the reaction. If the negative block is 0.5 percent of sessions, it may be a thin residue of unusual traffic and the right response is to check whether it even survives a re-run from a different initialisation. If it is a fifth of the sessions, the partition itself is wrong. ### The cluster with uniformly short bars Scores clustered just above zero mean cohesion and separation are nearly equal for every member. The group is real enough to be assigned, but it lives in the frontier between two better-defined clusters — the residue left over once the distinct groups have claimed their points. It is not a small cluster, note; smallness would show as a short block, not as short bars. A boundary cluster like this is usually the least actionable segment of the set, because nothing about it is distinct. ### Why the average misled The overall silhouette is a mean over points, so a large, clean, well-separated cluster contributes many strongly positive values and can hold the headline number up while two other clusters are failing. Reporting per-cluster means is the minimum fix. Even that is not enough on its own: a cluster in which half the points score 0.8 and half score -0.1 averages roughly the same as one where every point scores 0.35, and those are very different situations. The distribution is the object of interest; the plot is how you see it. ### What to do with the diagnosis Read the per-cluster means and block heights together. Identify the preferred neighbour of the negative points, and treat the overlapping pair as a single candidate group unless there is a reason outside the geometry to keep them apart. Check whether the features are on comparable scales, since one dominating feature manufactures exactly this pattern — long thin regions carved arbitrarily. Re-run from several initialisations and see whether the negative block reappears in the same place; a defect that moves is an artefact of initialisation, a defect that stays is in the data. And be clear about what the plot cannot tell you: it evaluates geometry only, so a partition can look immaculate here and still be useless for the decision it was built to support.