Joint Multidimensional Scaling

The repository implements the Joint Multidimensional Scaling (Joint MDS) described in the following paper:

Dexiong Chen, Bowen Fan, Carlos Oliver, Karsten Borgwardt. Unsupervised Manifold Alignment with Joint Multidimensional Scaling. ICLR 2023

Joint MDS is a an approach for unsupervised manifold alignment, which maps datasets from two different domains without any known correspondences between data instances across the datasets, to a common low-dimensional Euclidean space. Joint MDS integrates Multidimensional Scaling (MDS) and Wasserstein Procrustes analysis into a joint optimization problem to simultaneously generate isometric embeddings of data and learn correspondences between instances from two different datasets, while only requiring intra-dataset pairwise dissimilarities as input.

Installation

The dependencies are managed by miniconda

python=3.9
numpy
scipy
pytorch=1.9.1
scikit-learn
pandas

To start with the package, run

export $PYTHONPATH=$PWD

Citation

Please use the following to cite our work:

@inproceedings{chenunsupervised,
  title={Unsupervised Manifold Alignment with Joint Multidimensional Scaling},
  author={Chen, Dexiong and Fan, Bowen and Oliver, Carlos and Borgwardt, Karsten},
  booktitle={International Conference on Learning Representations},
  year={2023}
}

Usage

The usage of Joint MDS is similar to the MDS function in scikit-learn. Here is one minimal example of Joint MDS.

from joint_mds import JointMDS
import numpy as np

D1 = np.random.rand(128, 10)
D2 = np.random.rand(64, 20) 

JMDS = JointMDS(n_components=2, dissimilarity="euclidean")
Z1, Z2, P = JMDS.fit_transform(D1, D2)

print(Z1.shape) # (128, 2)
print(Z2.shape) # (64, 2)
print(P.shape)  # (128, 64)

Reproducing results in our paper

Data

All our experimental scripts are in the folder experiments. So to start with, first run

cd datasets
bash get_data.sh

Then cd ../examples

Joint visualization and unsupervised heterogeneous domain adaptation

For sythetic datasets, run

python example_simulation.py --dataset s1 --components 2

The dataset can be either s1, s2 or s3 respectively for bifurcation, Swiss roll and circular frustum.

For real-world datasets, run

# scGEM
python example_scGEM.py --components 2

# SNAREseq
python example_SNAREseq.py --components 2

# MNIST-USPS
python example_mnist_usps.py --components 2

Graph matching

For PPI network matching, the target graph has 5%, 15% or 25% additonal noisy edges. For example, for matching 5% noise graph, run

python example_matching_PPI.py --noise 5

For MIMIC graph matching task, run

python example_matching_MIMIC.py

Protein structure alignment

Run

python example_protein_alignment.py

For all paramters in Joint MDS please refer to joint_mds.py.

Funding

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 813533 (K.B.).