Weird behaviour when using transform on new data

Nobody has claimed this yet.

I have encountered a very strange behaviour when trying to use UMAP for a fairly simple feature learning scenario.

As a minimal example, I took the digits code from the tutorial and modified it a little in the following way instead of the usual split:

- The training points are now those whose labels are < 9.
- The test points are those with label 9.

This is the code:
```python
import numpy as np
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split, cross_val_score
from sklearn.neighbors import KNeighborsClassifier
from sklearn.svm import SVC

import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

import umap

sns.set(context='notebook', style='white', rc={'figure.figsize':(14,10)})

digits = load_digits()

X_train, X_test, y_train, y_test = train_test_split(digits.data,
digits.target,
stratify=digits.target,
random_state=42)
print(X_train.shape, X_test.shape)

i1 = np.where(digits.target<9)[0]
i2 = np.where(digits.target==9)[0]

X_train = digits.data[i1,:]
y_train = digits.target[i1]
X_test = digits.data[i2,:]
y_test = digits.target[i2]

print(X_train.shape, X_test.shape)

trans = umap.UMAP(n_neighbors=15, random_state=42).fit(X_train, y_train)

plt.scatter(trans.embedding_[:, 0], trans.embedding_[:, 1], s= 5, c=y_train, cmap='Spectral')
plt.title('Embedding of the training set by UMAP', fontsize=24);

test_embedding = trans.transform(X_test)

alldata = np.concatenate((trans.embedding_, test_embedding))
yy = np.concatenate((y_train, y_test))

plt.scatter(alldata[:, 0], alldata[:, 1], s= 5, c=yy, cmap='Spectral')
plt.title('Now apply the transform to the test and plot all together:', fontsize=24);
```

The result is very strange:

It seems as if the training data is somehow mixed up with the transformation of the completely unrelated test data. The same thing happens with other data as well.

Is this a bug?

Start by running the provided Python digits example, focusing on UMAP(...).fit(X_train, y_train) and trans.transform(X_test). Compare the training embedding and transformed test points in the separate and combined plots. Done means determining whether the observed mixing is expected behavior or a reproducible transform bug.

Written by the indexing model from the issue text.