chor-nyan/trimap

TriMap: Dimensionality Reduction Using Triplet Constraints

TriMap

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 reprsesentation 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 enjoys a transformer API similiar 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)

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).
• lr: Learning rate (default = 1000.0).
• n_iters: Number of iterations (default = 400).

The other parameters include:

• weight_adj: Adjust weights for extreme outliers using a log-transformation (default = True).
• 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. For more results, please refer to our paper.

MNIST Handwritten Digits (n = 70,000, d = 784)

Fashion MNIST (n = 70,000, d = 784)

Tabula Muris (n = 53,760, d = 23,433)

TV News (n = 129,685, d = 50)

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: [email protected]. 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.