Note

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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 `annoy`

and `nmslib`

to
replace KNeighborsTransformer and perform approximate nearest neighbors.
These packages can be installed with `pip install annoy nmslib`

.

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 wrappers.

Sample output:

```
Benchmarking on MNIST_2000:
---------------------------
AnnoyTransformer: 0.583 sec
NMSlibTransformer: 0.321 sec
KNeighborsTransformer: 1.225 sec
TSNE with AnnoyTransformer: 4.903 sec
TSNE with NMSlibTransformer: 5.009 sec
TSNE with KNeighborsTransformer: 6.210 sec
TSNE with internal NearestNeighbors: 6.365 sec
Benchmarking on MNIST_10000:
----------------------------
AnnoyTransformer: 4.457 sec
NMSlibTransformer: 2.080 sec
KNeighborsTransformer: 30.680 sec
TSNE with AnnoyTransformer: 30.225 sec
TSNE with NMSlibTransformer: 43.295 sec
TSNE with KNeighborsTransformer: 64.845 sec
TSNE with internal NearestNeighbors: 64.984 sec
```

```
# Author: Tom Dupre la Tour
#
# License: BSD 3 clause
import time
import sys
try:
import annoy
except ImportError:
print("The package 'annoy' is required to run this example.")
sys.exit()
try:
import nmslib
except ImportError:
print("The package 'nmslib' is required to run this example.")
sys.exit()
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import NullFormatter
from scipy.sparse import csr_matrix
from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.neighbors import KNeighborsTransformer
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.datasets import fetch_openml
from sklearn.pipeline import make_pipeline
from sklearn.manifold import TSNE
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)
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
results = self.nmslib_.knnQueryBatch(X, k=n_neighbors, num_threads=self.n_jobs)
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
class AnnoyTransformer(TransformerMixin, BaseEstimator):
"""Wrapper for using annoy.AnnoyIndex as sklearn's KNeighborsTransformer"""
def __init__(self, n_neighbors=5, metric="euclidean", n_trees=10, search_k=-1):
self.n_neighbors = n_neighbors
self.n_trees = n_trees
self.search_k = search_k
self.metric = metric
def fit(self, X):
self.n_samples_fit_ = X.shape[0]
self.annoy_ = annoy.AnnoyIndex(X.shape[1], metric=self.metric)
for i, x in enumerate(X):
self.annoy_.add_item(i, x.tolist())
self.annoy_.build(self.n_trees)
return self
def transform(self, X):
return self._transform(X)
def fit_transform(self, X, y=None):
return self.fit(X)._transform(X=None)
def _transform(self, X):
"""As `transform`, but handles X is None for faster `fit_transform`."""
n_samples_transform = self.n_samples_fit_ if X is None else 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
indices = np.empty((n_samples_transform, n_neighbors), dtype=int)
distances = np.empty((n_samples_transform, n_neighbors))
if X is None:
for i in range(self.annoy_.get_n_items()):
ind, dist = self.annoy_.get_nns_by_item(
i, n_neighbors, self.search_k, include_distances=True
)
indices[i], distances[i] = ind, dist
else:
for i, x in enumerate(X):
indices[i], distances[i] = self.annoy_.get_nns_by_vector(
x.tolist(), n_neighbors, self.search_k, include_distances=True
)
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 test_transformers():
"""Test that AnnoyTransformer and KNeighborsTransformer give same results"""
X = np.random.RandomState(42).randn(10, 2)
knn = KNeighborsTransformer()
Xt0 = knn.fit_transform(X)
ann = AnnoyTransformer()
Xt1 = ann.fit_transform(X)
nms = NMSlibTransformer()
Xt2 = nms.fit_transform(X)
assert_array_almost_equal(Xt0.toarray(), Xt1.toarray(), decimal=5)
assert_array_almost_equal(Xt0.toarray(), Xt2.toarray(), decimal=5)
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]
def run_benchmark():
datasets = [
("MNIST_2000", load_mnist(n_samples=2000)),
("MNIST_10000", load_mnist(n_samples=10000)),
]
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(
perplexity=perplexity,
method="barnes_hut",
random_state=42,
n_iter=n_iter,
square_distances=True,
)
transformers = [
("AnnoyTransformer", AnnoyTransformer(n_neighbors=n_neighbors, metric=metric)),
(
"NMSlibTransformer",
NMSlibTransformer(n_neighbors=n_neighbors, metric=metric),
),
(
"KNeighborsTransformer",
KNeighborsTransformer(
n_neighbors=n_neighbors, mode="distance", metric=metric
),
),
(
"TSNE with AnnoyTransformer",
make_pipeline(
AnnoyTransformer(n_neighbors=n_neighbors, metric=metric),
TSNE(metric="precomputed", **tsne_params),
),
),
(
"TSNE with NMSlibTransformer",
make_pipeline(
NMSlibTransformer(n_neighbors=n_neighbors, metric=metric),
TSNE(metric="precomputed", **tsne_params),
),
),
(
"TSNE with KNeighborsTransformer",
make_pipeline(
KNeighborsTransformer(
n_neighbors=n_neighbors, mode="distance", metric=metric
),
TSNE(metric="precomputed", **tsne_params),
),
),
("TSNE with internal NearestNeighbors", TSNE(metric=metric, **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 = "Benchmarking on %s:" % dataset_name
print("\n%s\n%s" % (msg, "-" * len(msg)))
for transformer_name, transformer in transformers:
start = time.time()
Xt = transformer.fit_transform(X)
duration = time.time() - start
# print the duration report
longest = np.max([len(name) for name, model in transformers])
whitespaces = " " * (longest - len(transformer_name))
print("%s: %s%.3f sec" % (transformer_name, whitespaces, duration))
# plot TSNE embedding which should be very similar across methods
if "TSNE" in transformer_name:
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()
if __name__ == "__main__":
test_transformers()
run_benchmark()
```

**Total running time of the script:** ( 0 minutes 0.000 seconds)