By Michela Tjan

_{To learn more about the Open Visualization Academy (OVA), visit https://openvisualizationacademy.org}

Imagine you have thousands of things— books, images, documents, products, people, or pieces of text— and each one is described by hundreds or thousands of numbers.

This is what we mean by high-dimensional data. Each observation has many features, or dimensions, that describe it. A document might be represented by hundreds of numbers capturing aspects of its meaning. An image might have thousands of measurements describing its pixels or features.

The problem is that we can't easily look at 500 dimensions at once.

So we turn to visualization.

Techniques such as PCA, t-SNE, and UMAP help us take data with many dimensions and represent it in two or three dimensions so we can see it. This is one reason they've become so popular in data science and increasingly in visualization projects.

You may have seen examples such as Google's A.I. Experiments: t-SNE Map, Ocean of Books, or MarketMap. These projects use dimensionality-reduction techniques to turn complicated datasets into visual spaces that people can explore, which have been incredibly useful.

But there's a catch.

When a visualization produces a beautiful landscape of distinct groups, it's tempting to think we've discovered those groups hiding inside the data. For example, four distinct clusters appear, neatly separated, with a couple sitting close enough to suggest a relationship. It feels like you've uncovered something meaningful.

Maybe you have.

But it's worth remembering that the visualization is also doing exactly what it was designed to do: constructing a low-dimensional representation of a much more complicated dataset.

PCA, UMAP, and t-SNE make different choices about what information to preserve.

PCA looks for directions that capture the most variation in the data. UMAP and t-SNE focus more heavily on local neighborhoods: which observations are close to one another in the original high-dimensional space.

They then try to arrange those relationships in two dimensions.

That means a UMAP or t-SNE plot is particularly useful for seeing who is near whom.

But other visual properties can be misleading.

A cluster that looks larger isn't necessarily larger or denser in the original data. Two clusters that look close together aren't necessarily similar in the original space. And under some settings, even data without meaningful clusters can produce convincing-looking groups.

None of this means the visualization is wrong.

It means we shouldn't assume that everything we can see in the picture corresponds directly to something in the data.

There isn't one universally "correct" UMAP or t-SNE visualization.

Change parameters such as t-SNE's perplexity or UMAP's n_neighbors and min_dist, and the resulting picture can change substantially. Clusters can split, merge, or become more or less distinct.

Even the same dataset can produce very different-looking structures under different settings.

That's why a pattern that appears in only one configuration deserves some skepticism.

If the structure is real, we should expect to find supporting evidence beyond one particular projection.

No.

UMAP and t-SNE are excellent exploratory tools. They can help us find potential groups, spot outliers, explore machine-learning embeddings, and discover patterns worth investigating.

The important distinction is between using the visualization to ask questions and using it to answer them.

If a UMAP plot appears to show five groups, go back to the underlying data. Check whether the pattern persists with different settings. Look at labeled examples. Compare it with clustering methods or other analyses.

A visualization can give you a useful hypothesis.

It just shouldn't be the evidence that proves the hypothesis.

A good UMAP can reveal interesting structure, but it doesn't prove that structure exists.

The map isn't the territory. And sometimes the most interesting part is finding out what the territory actually looks like.