Author here.
I built this because I needed to run dimensionality reduction entirely in the browser (client-side) for an interactive tool. The standard options (UMAP, t-SNE) were either too heavy for JS/WASM or required a GPU backend to run at acceptable speeds for interactive use.
This approach ("Sine Landmark Reduction") uses linearised trilateration—similar to GPS positioning—against a synthetic "sine skeleton" of landmarks.
The main trade-offs:
It is O(N) and deterministic (solves Ax=b instead of iterative gradient descent).
It forces the topology onto a loop structure, so it is less accurate than UMAP for complex manifolds (like Swiss Rolls), but it guarantees a clean layout for user interfaces.
It can project ~9k points (50 dims) to 3D in about 2 seconds on a laptop CPU. Python implementation and math details are in the post. Happy to answer questions!
Something seems off here. t-SNE should not be taking 15-25 seconds for only 5k points and 20 dimensions, but rather somewhere like 1-2 seconds. Also since the given alternative is not as good, you would probably be able to reduce the iterations somewhat with t-SNE if speed is wanted at the risk of quality. Alternatively UMAP for this would be milliseconds, bordering on real-time with aggressive tuning.
The claim of linear runtime is only true if K is independent of the dataset size, so it would have been nice to see an exploration of how different values of K impact results. I.e. does clustering get better for larger K, if so how much? The values 50 and 100 seem arbitrary and even suspiciously close to sqrt(N) for the 9K dataset.
Glad to see 2d mapping is still of interest. 20 years ago, information visualization, data cartography, exploratory analytics, etc.. was pretty alive, but it never really took off and found a reliable niche in the industry, or real end user application. Why map it, when the machine can just tell you.
Would be nice to see it come back. Would love to browse for books and movies on maps again, rather that getting lists regurgitated at me.
8 comments
[ 0.19 ms ] story [ 45.3 ms ] threadThis approach ("Sine Landmark Reduction") uses linearised trilateration—similar to GPS positioning—against a synthetic "sine skeleton" of landmarks.
The main trade-offs:
It is O(N) and deterministic (solves Ax=b instead of iterative gradient descent).
It forces the topology onto a loop structure, so it is less accurate than UMAP for complex manifolds (like Swiss Rolls), but it guarantees a clean layout for user interfaces.
It can project ~9k points (50 dims) to 3D in about 2 seconds on a laptop CPU. Python implementation and math details are in the post. Happy to answer questions!
UMAP is not O(n^2) it is O(n log n).
Would be nice to see it come back. Would love to browse for books and movies on maps again, rather that getting lists regurgitated at me.