Slow fit for small datasets using UMAP or densMAP

Is it normal for UMAP or densMAP to take 5-40 s to fit a small dataset of precomputed distances (e.g. 10x10 distance matrix)? My "test" scripts for a separate project which include a couple of UMAP calls end up taking about as much time as if I used a 10000 x 10000 distance matrix.

Reproducible script:

"""Time various calls to UMAP."""
import umap
import numpy as np
from time import time
from scipy.spatial.distance import pdist, squareform


class Timer(object):
    """
    Simple timer class.

    https://stackoverflow.com/a/5849861/13697228
    Usage
    -----
    with Timer("description"):
        # do stuff
    """

    def __init__(self, name=None):
        """Record name."""
        self.name = name

    def __enter__(self):
        """Enter the timer."""
        self.tstart = time()

    def __exit__(self, type, value, traceback):
        """Exit the timer."""
        if self.name:
            print(
                "[%s]" % self.name,
            )
        print(("Elapsed: {}\n").format(round((time() - self.tstart), 5)))


X = np.random.rand(10, 5)

eucl_dm = squareform(pdist(X))

# fmt: off
# Earth Mover's Distance matrix (not related to X)
emd_dm = np.array([[ 0.        , 27.        , 27.        ,  6.86666667, 15.        ,
        19.65      , 10.8       , 15.6       ,  9.71428571, 19.6       ],
       [27.        ,  0.        , 14.5       , 26.66666667, 20.6       ,
        20.25      , 35.        , 19.        , 19.42857143, 25.        ],
       [27.        , 14.5       ,  0.        , 23.33333333, 14.2       ,
        11.25      , 24.        , 18.6       , 18.42857143, 25.        ],
       [ 6.86666667, 26.66666667, 23.33333333,  0.        , 12.66666667,
        18.41666667, 13.        , 13.26666667,  9.57142857, 16.33333333],
       [15.        , 20.6       , 14.2       , 12.66666667,  0.        ,
         8.15      , 18.8       , 19.4       , 16.42857143, 24.6       ],
       [19.65      , 20.25      , 11.25      , 18.41666667,  8.15      ,
         0.        , 19.75      , 23.85      , 17.53571429, 29.25      ],
       [10.8       , 35.        , 24.        , 13.        , 18.8       ,
        19.75      ,  0.        , 24.6       , 17.71428571, 29.        ],
       [15.6       , 19.        , 18.6       , 13.26666667, 19.4       ,
        23.85      , 24.6       ,  0.        ,  9.02857143,  6.8       ],
       [ 9.71428571, 19.42857143, 18.42857143,  9.57142857, 16.42857143,
        17.53571429, 17.71428571,  9.02857143,  0.        , 13.42857143],
       [19.6       , 25.        , 25.        , 16.33333333, 24.6       ,
        29.25      , 29.        ,  6.8       , 13.42857143,  0.        ]]) #
# fmt: on

with Timer("Euclidean UMAP"):
    umap.UMAP().fit(X)

with Timer("Precomputed Euclidean UMAP"):
    umap.UMAP(metric="precomputed").fit(eucl_dm)

with Timer("Precomputed EMD UMAP"):
    umap.UMAP(metric="precomputed").fit(emd_dm)

with Timer("Precomputed EMD densMAP"):
    umap_trans = umap.UMAP(
        densmap=True,
        output_dens=True,
        dens_lambda=1.0,
        min_dist=0.01,
        n_components=2,
        metric="precomputed",
    ).fit(emd_dm)

with Timer("Precomputed EMD densMAP"):
    std_trans = umap.UMAP(
        densmap=True,
        output_dens=True,
        dens_lambda=1.0,
        metric="precomputed",
    ).fit(emd_dm)

with Timer("Precomputed EMD UMAP"):
    std_trans = umap.UMAP(metric="precomputed").fit(emd_dm)

Output:

C:\Users\sterg\Anaconda3\envs\elm2d-crabnet\lib\site-packages\umap\umap_.py:2213: UserWarning: n_neighbors is larger than the dataset size; truncating to X.shape[0] - 1
  warn(
[Euclidean UMAP]
Elapsed: 14.15193

C:\Users\sterg\Anaconda3\envs\elm2d-crabnet\lib\site-packages\umap\umap_.py:1735: UserWarning: using precomputed metric; transform will be unavailable for new data and inverse_transform will be unavailable for all data
  warn(
C:\Users\sterg\Anaconda3\envs\elm2d-crabnet\lib\site-packages\umap\umap_.py:2213: UserWarning: n_neighbors is larger than the dataset size; truncating to X.shape[0] - 1
  warn(
[Precomputed Euclidean UMAP]
Elapsed: 8.00694

C:\Users\sterg\Anaconda3\envs\elm2d-crabnet\lib\site-packages\umap\umap_.py:1735: UserWarning: using precomputed metric; transform will be unavailable for new data and inverse_transform will be unavailable for all data
  warn(
C:\Users\sterg\Anaconda3\envs\elm2d-crabnet\lib\site-packages\umap\umap_.py:2213: UserWarning: n_neighbors is larger than the dataset size; truncating to X.shape[0] - 1
  warn(
[Precomputed EMD UMAP]
Elapsed: 4.76215

C:\Users\sterg\Anaconda3\envs\elm2d-crabnet\lib\site-packages\umap\umap_.py:1735: UserWarning: using precomputed metric; transform will be unavailable for new data and inverse_transform will be unavailable for all data
  warn(
C:\Users\sterg\Anaconda3\envs\elm2d-crabnet\lib\site-packages\umap\umap_.py:2213: UserWarning: n_neighbors is larger than the dataset size; truncating to X.shape[0] - 1
  warn(
[Precomputed EMD densMAP]
Elapsed: 28.30055

C:\Users\sterg\Anaconda3\envs\elm2d-crabnet\lib\site-packages\umap\umap_.py:1735: UserWarning: using precomputed metric; transform will be unavailable for new data and inverse_transform will be unavailable for all data
  warn(
C:\Users\sterg\Anaconda3\envs\elm2d-crabnet\lib\site-packages\umap\umap_.py:2213: UserWarning: n_neighbors is larger than the dataset size; truncating to X.shape[0] - 1
  warn(
[Precomputed EMD densMAP]
Elapsed: 11.316

C:\Users\sterg\Anaconda3\envs\elm2d-crabnet\lib\site-packages\umap\umap_.py:1735: UserWarning: using precomputed metric; transform will be unavailable for new data and inverse_transform will be unavailable for all data
  warn(
C:\Users\sterg\Anaconda3\envs\elm2d-crabnet\lib\site-packages\umap\umap_.py:2213: UserWarning: n_neighbors is larger than the dataset size; truncating to X.shape[0] - 1
  warn(
[Precomputed EMD UMAP]
Elapsed: 5.19057

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