A t-SNE plot of 5,000 return vectors shows four tight, well-separated clusters. State three specific conclusions you may not draw from this plot and explain the property of the algorithm that…

Question

A t-SNE plot of 5,000 return vectors shows four tight, well-separated clusters. State three specific conclusions you may not draw from this plot and explain the property of the algorithm that invalidates each.

Accepted Answer

You may not conclude that the distances between clusters are meaningful, that the cluster sizes reflect the spread of the underlying groups, or that four is the number of groups in the data, because t-SNE optimises a divergence between neighbour probability distributions that only constrains local structure. The objective matches a Gaussian neighbour distribution in the original space to a heavy-tailed one in two dimensions, so points that are near stay near, while the placement of well-separated groups relative to each other is essentially arbitrary and changes between random seeds. Cluster sizes are set by the algorithm expanding dense regions and contracting sparse ones to equalise the local neighbour probabilities, so a tight cluster on the plot can be a diffuse group in the data. The number of visible clumps depends strongly on the perplexity: at low perplexity the method sees only nearest neighbours and shatters a single group into fragments, and at high perplexity it merges distinct groups, so a cluster count read off one setting is not a property of the data. The defensible use is as a visual check of structure that is then tested by a method with a criterion, such as clustering in the original space with a stability measure, or a supervised test that the putative groups predict something out of sample.