FastMapy

FastMapy is a Python implementation of the FastMap¹ multidimensional-scaling technique. It embeds objects into a vector space from a supplied distance metric, attempting to preserve their relative distances.

This package has common distance metrics already defined and ready to use over appropriate objects, such as Jaccard distance over character shingled n-gram strings or Levenshtein edit distance for embedding string objects. Euclidean distance and taxi cab distance are also available for vector objects. Dictionary objects also work assuming a sparse vector style dictionary of {index: count} where index can be an actual vector index or a token and its occurrence count.

Threaded execution can be enabled for model building and object transformation with the cores argument. It is set to serial execution (cores=1) by default. The benefit depends on the distance metric and runtime.

Installation

python -m pip install FastMapy

For local development:

python -m pip install -e '.[dev]'
pytest

Optional features can be installed individually with FastMapy[metrics] or FastMapy[plots], or together with FastMapy[all]. t-SNE and UMAP are included only in the plotting extra.

Usage

from fastmap.distances import Jaccard
import fastmap

fm_model = fastmap.FastMap(dim=8, distance=Jaccard, dist_args={'shingle_size':4})

embedding = fm_model.fit_transform(string_data)

The target vector space is eight-dimensional and strings are shingled into four-grams before their distances are computed. fit_transform returns one NumPy array per input object.

fit requires more training objects than requested dimensions. transform expects a collection of objects; wrap a single dense vector in a one-element collection, such as model.transform([[1.0, 2.0]]).

Metrics

fastmap.metrics provides a pairwise-distance helper plus normalized stress, Pearson/Spearman distance correlation, and trustworthiness. Pass the original pairwise-distance matrix and the resulting embedding to the evaluators. Spearman correlation requires the metrics extra.

from fastmap.metrics import distance_correlation, pairwise_distances, trustworthiness

original_distances = pairwise_distances(string_data, Jaccard(shingle_size=4))
print(distance_correlation(original_distances, embedding))
print(trustworthiness(original_distances, embedding, n_neighbors=5))

Plots

fastmap.plots.plot_embedding renders 2D or 3D embeddings. For embeddings with more dimensions, reduce_for_plot performs a visualization-only t-SNE or UMAP reduction; it does not train or stack another FastMap model. These helpers require the plots extra.

from fastmap.plots import plot_embedding, reduce_for_plot

plot_embedding(embedding_2d, dimensions=2)
plot_embedding(embedding_3d, dimensions=3)

umap_2d = reduce_for_plot(embedding, method="umap", n_components=2)
plot_embedding(umap_2d, dimensions=2)

Reproducibility

FastMap selects an initial pivot randomly for each dimension. Consequently, unseeded fits are intentionally non-deterministic: two fits over identical data can produce different, valid embeddings. Tests and experiments that need repeatability should control Python's random-number generator before fitting.

Built-in metrics

cores enables threaded fitting and transformation. It defaults to 1; any speedup depends on the distance metric and runtime.

Fitting a batch of distinct models

Use FastMap.fit_many to fit several models with identical settings against one training collection:

models = fastmap.FastMap.fit_many(
    string_data,
    count=4,
    dim=8,
    distance=Jaccard,
    dist_args={"shingle_size": 4},
)

Each model starts every dimension from a distinct training-object index. The batch also avoids reusing an unordered pivot pair anywhere in the batch. If a pair collides, FastMap retries that dimension with another unused starting point and retains all prior dimensions. When no distinct pair can be found within pair_retries attempts, the collision is retained and reported by the model's pivot_pair_collisions property. count cannot exceed the number of training objects.

References

1 Proceedings of the 1995 ACM SIGMOD international conference on Management of data - SIGMOD ’95. (1995). doi:10.1145/223784 ↩