Fast Laplacian Eigenmaps in python

Open-source Laplacian Eigenmaps for dimensionality reduction of large data in python. Comes with an
wrapper for NMSlib to compute approximate-nearest-neighbors.
Performs several times faster than the default scikit-learn implementation.

Installation

You’ll need NMSlib for using this package properly. Installing it with no binaries is recommended if your CPU supports
advanced instructions (it problably does):

pip3 install --no-binary :all: nmslib
# Along with requirements:
pip3 install numpy pandas scipy scikit-learn

Then you can install this package with pip:

pip3 install fastlapmap

Usage

See the following example with the handwritten digits data.
Here, I visually compare results from the scikit-learn Laplacian Eigenmaps
implementation to
those from my implementation.

Note that this implementation contains two similarity-learning algorithms: anisotropic diffusion maps and fuzzy simplicial sets.

# Import libraries
import numpy as np
import matplotlib.pyplot as plt
from sklearn.manifold import SpectralEmbedding
from fastlapmap import LapEigenmap

# Load some data
from sklearn.datasets import load_digits
digits = load_digits()
data = digits.data

# Define hyperparameters
N_EIGS=2
N_NEIGHBORS=10
N_JOBS=10

sk_se = SpectralEmbedding(n_components=N_EIGS, n_neighbors=N_NEIGHBORS, n_jobs=N_JOBS).fit_transform(data)

flapmap_diff = LapEigenmap(data, n_eigs=2, similarity='diffusion', norm_laplacian=True, k=N_NEIGHBORS, n_jobs=N_JOBS)
flapmap_fuzzy = LapEigenmap(data, n_eigs=2, similarity='fuzzy', norm_laplacian=True, k=N_NEIGHBORS, n_jobs=N_JOBS)

fig, (ax1, ax2, ax3) = plt.subplots(1, 3)
fig.suptitle('Handwritten digits data:', fontsize=24)
ax1.scatter(sk_se[:, 0], sk_se[:, 1], c=digits.target, cmap='Spectral', s=5)
ax1.set_title('Sklearn\'s Laplacian Eigenmaps', fontsize=20)
ax2.scatter(flapmap_diff[:, 0], flapmap_diff[:, 1], c=digits.target, cmap='Spectral', s=5)
ax2.set_title('Fast Laplacian Eigenmaps with diffusion harmonics', fontsize=20)
ax3.scatter(flapmap_fuzzy[:, 0], flapmap_fuzzy[:, 1], c=digits.target, cmap='Spectral', s=5)
ax3.set_title('Fast Laplacian Eigenmaps with fuzzy simplicial sets', fontsize=20)
plt.show()

As we can see, results are nearly identical.

Benchmark

See the runtime comparison between this implementation and scikit-learn:

## Load benchmark function:
from fastlapmap.benchmark import runtime_benchmark

# Load data
from sklearn.datasets import load_digits
digits = load_digits()
data = digits.data

# Define hyperparameters
N_EIGS = 2
N_NEIGHBORS = 10
N_JOBS = 10
SIZES = [1000, 5000, 10000, 25000, 50000, 100000]
N_RUNS = 3

runtime_benchmark(data,
                  n_eigs=N_EIGS,
                  n_neighbors=N_NEIGHBORS,
                  n_jobs=N_JOBS,
                  sizes=SIZES,
                  n_runs=N_RUNS)

As you can see, the diffusion harmoics model is the fastest, followed closely by fuzzy simplicial sets. Both outperform
scikit-learn default implementation and escalate linearly with sample size.