TriMap: Large-scale Dimensionality Reduction Using Triplets
Project description
TriMap is a dimensionality reduction method that uses triplet constraints to form a low dimensional embedding of a set of points. The triplet constraints are of the form “point i is closer to point j than point k”. The triplets are sampled from the high-dimensional representation of the points and a weighting scheme is used to reflect the importance of each triplet.
TriMap provides a much better global view of the data than the other dimensionality reduction methods such t-SNE, LargeVis, and UMAP. The global structure includes relative distances of the clusters, multiple scales in the data, and the existence of possible outliers.
The following implementation is in Python.
How to use TriMap
TriMap has a transformer API similar to other sklearn libraries. To use TriMap with the default parameters, simply do:
import trimap
from sklearn.datasets import load_digits
digits = load_digits()
embedding = trimap.TRIMAP().fit_transform(digits.data)
To calculate the global score, do:
gs = trimap.TRIMAP(verbose=False).global_score(digits.data, embedding)
print("global score %2.2f" % gs)
Parameters
Unlike other dimensionality reduction method, TriMap only has a few parameters to tune:
n_inliers: Number of nearest neighbors for forming the nearest neighbor triplets (default = 10).
n_outliers: Number of outliers for forming the nearest neighbor triplets (default = 5).
n_random: Number of random triplets per point (default = 5).
weight_adj: Adjust weights for extreme outliers using a log-transformation (default = 500.0).
lr: Learning rate (default = 1000.0).
n_iters: Number of iterations (default = 400).
The other parameters include:
fast_trimap: Use only ANNOY for nearest-neighbor search (default = True).
opt_method: Optimization method {‘sd’ (steepest descent), ‘momentum’ (GD with momentum), ‘dbd’ (delta-bar-delta, default)}.
verbose: Print the progress report (default = True).
return_seq: Store the intermediate results and return the results in a tensor (default = False).
An example of adjusting these parameters:
import trimap
from sklearn.datasets import load_digits
digits = load_digits()
embedding = trimap.TRIMAP(n_inliers=10,
n_outliers=5,
n_random=5).fit_transform(digits.data)
The nearest-neighbor calculation is performed by default using ANNOY. For more accurate results, the first 5 nearest-neighbors of each point can be calculated using sklearn.neighbors.NearestNeighbors and the results can be combined with those calculated using ANNOY. However, this may significantly increase the runtime. The fast_trimap (default = True) argument controls this property. For more accurate results, set fast_trimap = False.
Examples
The following are some results on real-world datasets. The values of nearest-neighbor accuracy and global score are shown as a pair (NN, GS) on top of each figure. For more results, please refer to our paper.
USPS Handwritten Digits (n = 11,000, d = 256)
20 News Groups (n = 18,846, d = 100)
Tabula Muris (n = 53,760, d = 23,433)
MNIST Handwritten Digits (n = 70,000, d = 784)
Fashion MNIST (n = 70,000, d = 784)
TV News (n = 129,685, d = 100)
Runtime of t-SNE, LargeVis, UMAP, and TriMap in the hh:mm:ss format on a single machine with 2.6 GHz Intel Core i5 CPU and 16 GB of memory is given in the following table. We limit the runtime of each method to 12 hours. Also, UMAP runs out of memory on datasets larger than ~4M points.
Installing
Requirements:
numpy
scikit-learn
numba
annoy
Install Options
If you have all the requirements installed, you can use pip:
sudo pip install trimap
Please regularly check for updates and make sure you are using the most recent version. If you have TriMap installed and would like to upgrade to the newer version, you can use the command:
sudo pip install --upgrade --force-reinstall trimap
An alternative is to install the dependencies manually using anaconda and using pip to install TriMap:
conda install numpy
conda install scikit-learn
conda install numba
conda install annoy
pip install trimap
For a manual install get this package:
wget https://github.com/eamid/trimap/archive/master.zip
unzip master.zip
rm master.zip
cd trimap-master
Install the requirements
sudo pip install -r requirements.txt
or
conda install scikit-learn numba annoy
Install the package
python setup.py install
Support and Contribution
This implementation is still a work in progress. Any comments/suggestions/bug-reports are highly appreciated. Please feel free contact me at: eamid@ucsc.edu. If you would like to contribute to the code, please fork the project and send me a pull request.
License
Please see the LICENSE file.
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