BMS5010 Chap.3 Unsupervised Learning: Clustering and Structure
Unsupervised Learning: Clustering and Structure
Learning with nothing to be wrong against
Unsupervised learning is defined in the course as the framework in which algorithms learn patterns exclusively from unlabelled data. You begin with a dataset carrying no labels at all and look for patterns that are interesting and useful, and four kinds are named: clusters of related points, outliers, denoised signals, and the groupings those produce.
The clinical illustrations are cancer subtyping from molecular features, image segmentation by grouping similar pixels, unusual vital-sign readings that might indicate an undiagnosed condition, and recovering an image corrupted by noise.
The absence of a label is not a minor difference, because it removes the column against which a prediction could be checked.
The comparison the course draws, row by row
Classification assigns predefined classes to instances and requires labelled data for training; clustering groups similar instances by their similarity and requires none.
The output of one is a class assignment, the output of the other a cluster assignment. The purpose of one is predicting the class of an unseen instance; the purpose of the other is discovering inherent patterns in what you already hold.
The last row is the one that carries marks in an answer: classification can be wrong in a way anyone can check against a held-back label, and clustering has nothing to disagree with, which is exactly the difficulty.
The choice rule the course gives follows from that.
Similarity has to be stated before anything is grouped
Looking at an unlabelled scatter you can guess that the data forms three groups without any formal definition of similarity. In an application you cannot: the measure used to compare two samples has to be named, expressed in that dataset's own features. The course gives two.
Straight-line distance across the features adds the squared gaps and so is dominated by whichever variable spans the larger range, which is a property of the units somebody chose rather than of the biology.
The angle between two feature vectors ignores magnitude entirely, so two patients with the same profile at different overall intensity are far apart under the first and identical under the second.
Standardise, then say that you did
Because straight-line distance is scale-sensitive, clustering an unstandardised table frequently reproduces a measurement scale rather than a patient type, and a reader cannot tell from the resulting picture that this happened.
Putting the features on a common scale before clustering is not optional, and recording it in the methods section is what allows someone else to reproduce the grouping. The cluster identifier that comes out is genuinely useful because it compresses a wide table into one label per row, but it carries none of the reasons.
Naming a cluster the severe group is a claim about something outside the clustering and needs evidence from outside it.
Two scores, answering different questions
The adjusted Rand index compares two clusterings of the same data, running from one for perfect agreement through zero for random agreement to negative values for worse than random, so it needs a second clustering to compare against and is only available when some known grouping exists.
The silhouette score needs nothing outside the data: it combines how close a point sits to its own group with how far it sits from the nearest other group, on a scale from minus one to one, where one means well separated groups, zero means overlapping ones, and negative values suggest points have been assigned to the wrong group.
Neither score tells you the groups mean anything clinically.
Dimension reduction, and why biology forces it
Dimension reduction reduces the number of input variables while preserving as much information as possible.
The course motivates it with the width of biological data, listing a genome of three billion base pairs, a transcriptome of roughly twenty to twenty-five thousand genes, thousands of proteins and hundreds to thousands of small molecules, and then names the curse of dimensionality directly: high dimensionality leads to overfitting, longer computation and data you cannot look at.
The worked illustration reduces single-cell expression data to two coordinates in which cells of the same type still land together. What survives is the grouping; the axes themselves carry no units and no meaning.
What this chapter covers
- 01
Unsupervised learning and the four kinds of pattern the course names
- 02
Classification against clustering, row by row, including how each can be wrong
- 03
Straight-line distance against the angle between feature vectors
- 04
Why scale decides a clustering before the algorithm runs
- 05
The cluster identifier as an output with no explanation attached
- 06
The adjusted Rand index and the silhouette score, and what each needs
- 07
Dimension reduction, the curse of dimensionality, and unitless axes
Say what a three-group plot has and has not established
- 3List the decisions that produced the picture.
- 3Name the scale problem in these two particular variables.
- 3State the defensible claim and the next analysis.
Key terms
- Cluster Identifier
- The single label assigned to each point after clustering, which compresses every feature the algorithm used and carries none of the reasons it used them.
- Cosine Similarity
- A comparison based on the angle between two feature vectors, which treats profiles of the same shape as identical regardless of their overall magnitude.
- Adjusted Rand Index
- A measure of agreement between two clusterings of the same data, where one means perfect agreement, zero means the agreement expected by chance, and negative values mean worse than chance.
- Curse Of Dimensionality
- The set of problems caused by having many input variables, including a greater tendency to overfit, longer computation and data that cannot be visualised.
- Cohesion
- How close a point sits to the other points in its own cluster, one of the two distances a silhouette score is built from.
Unsupervised Learning: Clustering and Structure FAQ
If clustering cannot be wrong, how is it ever evidence?
By being stable and by predicting something it was not given. Stability means the same grouping survives resampling, a different random start and a modest change to the feature set; a grouping that moves under any of those is a property of the run rather than of the patients. Prediction means the groups differ in a variable that was deliberately held out of the clustering, such as an outcome or a treatment response.
Neither check makes clustering a supervised method, and together they are the difference between a hypothesis and a finding.
How do I choose the number of clusters?
Not by looking for the best value, because there usually is not one. The silhouette score gives a defensible way to compare candidate values without needing any external truth, so computing it across a range and reporting the whole range is more informative than reporting the winner.
Beyond that, the number should be defensible clinically: a grouping that cannot be described to a clinician in a sentence each is not going to be used, however good its score. Report the score curve and your reasoning, not a single number presented as discovered.
When would I use dimension reduction rather than just dropping variables?
When the variables are individually weak and collectively informative, which is the normal situation in molecular data. Dropping variables keeps a subset in their original units, which stays interpretable and is the right move when a few are known to matter. Reduction builds new coordinates from combinations of all of them, which preserves more of the information and costs you the ability to say what any axis means.
That trade decides it: choose dropping when you need to name the variables in a discussion, and reduction when you need the picture or the downstream model to work at all.
Assessment move
Cluster the same small table twice, once on raw values and once on standardised ones, and look at how many patients change group. That single comparison teaches the scale lesson more durably than reading it, and the number of movers is a sentence you can use in a methods section. Then hold one variable out and test whether the groups differ on it, which is the move that turns a picture into evidence.
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