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Approximate nearest neighbors in TSNE¶

This example presents how to chain KNeighborsTransformer and TSNE in a pipeline. It also shows how to wrap the packages nmslib and pynndescent to replace KNeighborsTransformer and perform approximate nearest neighbors. These packages can be installed with pip install nmslib pynndescent.

Note: In KNeighborsTransformer we use the definition which includes each training point as its own neighbor in the count of n_neighbors, and for compatibility reasons, one extra neighbor is computed when mode == 'distance'. Please note that we do the same in the proposed nmslib wrapper.

# Author: Tom Dupre la Tour
# License: BSD 3 clause

First we try to import the packages and warn the user in case they are missing.

import sys

try:
    import nmslib
except ImportError:
    print("The package 'nmslib' is required to run this example.")
    sys.exit()

try:
    from pynndescent import PyNNDescentTransformer
except ImportError:
    print("The package 'pynndescent' is required to run this example.")
    sys.exit()

We define a wrapper class for implementing the scikit-learn API to the nmslib, as well as a loading function.

import joblib
import numpy as np
from scipy.sparse import csr_matrix

from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.datasets import fetch_openml
from sklearn.utils import shuffle


class NMSlibTransformer(TransformerMixin, BaseEstimator):
    """Wrapper for using nmslib as sklearn's KNeighborsTransformer"""

    def __init__(self, n_neighbors=5, metric="euclidean", method="sw-graph", n_jobs=-1):
        self.n_neighbors = n_neighbors
        self.method = method
        self.metric = metric
        self.n_jobs = n_jobs

    def fit(self, X):
        self.n_samples_fit_ = X.shape[0]

        # see more metric in the manual
        # https://github.com/nmslib/nmslib/tree/master/manual
        space = {
            "euclidean": "l2",
            "cosine": "cosinesimil",
            "l1": "l1",
            "l2": "l2",
        }[self.metric]

        self.nmslib_ = nmslib.init(method=self.method, space=space)
        self.nmslib_.addDataPointBatch(X.copy())
        self.nmslib_.createIndex()
        return self

    def transform(self, X):
        n_samples_transform = X.shape[0]

        # For compatibility reasons, as each sample is considered as its own
        # neighbor, one extra neighbor will be computed.
        n_neighbors = self.n_neighbors + 1

        if self.n_jobs < 0:
            # Same handling as done in joblib for negative values of n_jobs:
            # in particular, `n_jobs == -1` means "as many threads as CPUs".
            num_threads = joblib.cpu_count() + self.n_jobs + 1
        else:
            num_threads = self.n_jobs

        results = self.nmslib_.knnQueryBatch(
            X.copy(), k=n_neighbors, num_threads=num_threads
        )
        indices, distances = zip(*results)
        indices, distances = np.vstack(indices), np.vstack(distances)

        indptr = np.arange(0, n_samples_transform * n_neighbors + 1, n_neighbors)
        kneighbors_graph = csr_matrix(
            (distances.ravel(), indices.ravel(), indptr),
            shape=(n_samples_transform, self.n_samples_fit_),
        )

        return kneighbors_graph


def load_mnist(n_samples):
    """Load MNIST, shuffle the data, and return only n_samples."""
    mnist = fetch_openml("mnist_784", as_frame=False)
    X, y = shuffle(mnist.data, mnist.target, random_state=2)
    return X[:n_samples] / 255, y[:n_samples]

We benchmark the different exact/approximate nearest neighbors transformers.

import time

from sklearn.manifold import TSNE
from sklearn.neighbors import KNeighborsTransformer
from sklearn.pipeline import make_pipeline

datasets = [
    ("MNIST_10000", load_mnist(n_samples=10_000)),
    ("MNIST_20000", load_mnist(n_samples=20_000)),
]

n_iter = 500
perplexity = 30
metric = "euclidean"
# TSNE requires a certain number of neighbors which depends on the
# perplexity parameter.
# Add one since we include each sample as its own neighbor.
n_neighbors = int(3.0 * perplexity + 1) + 1

tsne_params = dict(
    init="random",  # pca not supported for sparse matrices
    perplexity=perplexity,
    method="barnes_hut",
    random_state=42,
    n_iter=n_iter,
    learning_rate="auto",
)

transformers = [
    (
        "KNeighborsTransformer",
        KNeighborsTransformer(n_neighbors=n_neighbors, mode="distance", metric=metric),
    ),
    (
        "NMSlibTransformer",
        NMSlibTransformer(n_neighbors=n_neighbors, metric=metric),
    ),
    (
        "PyNNDescentTransformer",
        PyNNDescentTransformer(
            n_neighbors=n_neighbors, metric=metric, parallel_batch_queries=True
        ),
    ),
]

for dataset_name, (X, y) in datasets:
    msg = f"Benchmarking on {dataset_name}:"
    print(f"\n{msg}\n" + str("-" * len(msg)))

    for transformer_name, transformer in transformers:
        longest = np.max([len(name) for name, model in transformers])
        start = time.time()
        transformer.fit(X)
        fit_duration = time.time() - start
        print(f"{transformer_name:<{longest}} {fit_duration:.3f} sec (fit)")
        start = time.time()
        Xt = transformer.transform(X)
        transform_duration = time.time() - start
        print(f"{transformer_name:<{longest}} {transform_duration:.3f} sec (transform)")
        if transformer_name == "PyNNDescentTransformer":
            start = time.time()
            Xt = transformer.transform(X)
            transform_duration = time.time() - start
            print(
                f"{transformer_name:<{longest}} {transform_duration:.3f} sec"
                " (transform)"
            )

Sample output:

Benchmarking on MNIST_10000:
----------------------------
KNeighborsTransformer  0.007 sec (fit)
KNeighborsTransformer  1.139 sec (transform)
NMSlibTransformer      0.208 sec (fit)
NMSlibTransformer      0.315 sec (transform)
PyNNDescentTransformer 4.823 sec (fit)
PyNNDescentTransformer 4.884 sec (transform)
PyNNDescentTransformer 0.744 sec (transform)

Benchmarking on MNIST_20000:
----------------------------
KNeighborsTransformer  0.011 sec (fit)
KNeighborsTransformer  5.769 sec (transform)
NMSlibTransformer      0.733 sec (fit)
NMSlibTransformer      1.077 sec (transform)
PyNNDescentTransformer 14.448 sec (fit)
PyNNDescentTransformer 7.103 sec (transform)
PyNNDescentTransformer 1.759 sec (transform)

Notice that the PyNNDescentTransformer takes more time during the first fit and the first transform due to the overhead of the numba just in time compiler. But after the first call, the compiled Python code is kept in a cache by numba and subsequent calls do not suffer from this initial overhead. Both KNeighborsTransformer and NMSlibTransformer are only run once here as they would show more stable fit and transform times (they don’t have the cold start problem of PyNNDescentTransformer).

import matplotlib.pyplot as plt
from matplotlib.ticker import NullFormatter

transformers = [
    ("TSNE with internal NearestNeighbors", TSNE(metric=metric, **tsne_params)),
    (
        "TSNE with KNeighborsTransformer",
        make_pipeline(
            KNeighborsTransformer(
                n_neighbors=n_neighbors, mode="distance", metric=metric
            ),
            TSNE(metric="precomputed", **tsne_params),
        ),
    ),
    (
        "TSNE with NMSlibTransformer",
        make_pipeline(
            NMSlibTransformer(n_neighbors=n_neighbors, metric=metric),
            TSNE(metric="precomputed", **tsne_params),
        ),
    ),
]

# init the plot
nrows = len(datasets)
ncols = np.sum([1 for name, model in transformers if "TSNE" in name])
fig, axes = plt.subplots(
    nrows=nrows, ncols=ncols, squeeze=False, figsize=(5 * ncols, 4 * nrows)
)
axes = axes.ravel()
i_ax = 0

for dataset_name, (X, y) in datasets:
    msg = f"Benchmarking on {dataset_name}:"
    print(f"\n{msg}\n" + str("-" * len(msg)))

    for transformer_name, transformer in transformers:
        longest = np.max([len(name) for name, model in transformers])
        start = time.time()
        Xt = transformer.fit_transform(X)
        transform_duration = time.time() - start
        print(
            f"{transformer_name:<{longest}} {transform_duration:.3f} sec"
            " (fit_transform)"
        )

        # plot TSNE embedding which should be very similar across methods
        axes[i_ax].set_title(transformer_name + "\non " + dataset_name)
        axes[i_ax].scatter(
            Xt[:, 0],
            Xt[:, 1],
            c=y.astype(np.int32),
            alpha=0.2,
            cmap=plt.cm.viridis,
        )
        axes[i_ax].xaxis.set_major_formatter(NullFormatter())
        axes[i_ax].yaxis.set_major_formatter(NullFormatter())
        axes[i_ax].axis("tight")
        i_ax += 1

fig.tight_layout()
plt.show()

Sample output:

Benchmarking on MNIST_10000:
----------------------------
TSNE with internal NearestNeighbors 24.828 sec (fit_transform)
TSNE with KNeighborsTransformer     20.111 sec (fit_transform)
TSNE with NMSlibTransformer         21.757 sec (fit_transform)

Benchmarking on MNIST_20000:
----------------------------
TSNE with internal NearestNeighbors 51.955 sec (fit_transform)
TSNE with KNeighborsTransformer     50.994 sec (fit_transform)
TSNE with NMSlibTransformer         43.536 sec (fit_transform)

We can observe that the default TSNE estimator with its internal NearestNeighbors implementation is roughly equivalent to the pipeline with TSNE and KNeighborsTransformer in terms of performance. This is expected because both pipelines rely internally on the same NearestNeighbors implementation that performs exacts neighbors search. The approximate NMSlibTransformer is already slightly faster than the exact search on the smallest dataset but this speed difference is expected to become more significant on datasets with a larger number of samples.

Notice however that not all approximate search methods are guaranteed to improve the speed of the default exact search method: indeed the exact search implementation significantly improved since scikit-learn 1.1. Furthermore, the brute-force exact search method does not require building an index at fit time. So, to get an overall performance improvement in the context of the TSNE pipeline, the gains of the approximate search at transform need to be larger than the extra time spent to build the approximate search index at fit time.

Finally, the TSNE algorithm itself is also computationally intensive, irrespective of the nearest neighbors search. So speeding-up the nearest neighbors search step by a factor of 5 would not result in a speed up by a factor of 5 for the overall pipeline.