Implicit-interval-Mapper

This repository implements optimization of a Mapper Algorithm with implicit intervals described in Tao, Yuyang, and Shufei Ge. "A Mapper Algorithm with implicit intervals and its optimization". The code files are released under the open source BSD 2-clause license.

All examples in the mannuscript are provided in a Jupyter notebook. The data folder contains the datasets used in the simulation studies, while the model folder contains the implementation of our proposed model.

Citation

If you use the code (partial or all) in your research, please cite the following manuscript:

Yuyang Tao and Shufei Ge. "A Mapper Algorithm with implicit intervals and its optimization"

Define a Mapper through Opt_GMM_Mapper class

You can easily define a GMM soft Mapper using the Opt_GMM_Mapper class. The input parameters required are the number of intervals and the initial parameters for a GMM model. We recommend fitting a GMM directly to the projected data and using these fitted parameters as the initial values.

from model import Opt_GMM_Mapper

# Inputs: number of intervals, initial parameters.
# We recommand use direclt fit a GMM on projected data as initial parameters.
m = Opt_GMM_Mapper(n_comp, means = init_mean, covariances=init_var, weights=init_weights)

Compute Mapper graph mode

Computing the Mapper graph mode is straightforward. A single step in the process can yield the distribution Q. Subsequently, the Mapper graph mode can be derived using the get_mode_graph() function, the return is a networkx graph.

# Compute the event probability matrix based on the  data, filtered (projected) data, and clustering scheme.
Q = m(projected_data, data, clustering)

# Get the Mapper graph mode
Mapper_graph_mode = m.get_mode_graph()

Optimization

Optimization is a standard process in PyTorch. To simplify the training process, we provide a Trainer class. The Trainer.fit(data, projected_data, l1, l2) method automatically completes the training, l1 and l2 is weight of loss function. While Trainer.analysis() offers a simple analysis of the training process, including the variation of the loss function.

import torch.optim.lr_scheduler as lr_scheduler
import torch.optim as optim
from model import Trainer

num_step = 200
l1 = 1 
l2 = 1 

# define optimizer and scheduler
optimizer = optim.SGD(m.parameters(), lr=0.001)
scheduler = lr_scheduler.StepLR(optimizer, step_size=100, gamma=0.1)

# mapper after optimization
Mapper_graph_mode_after = m.get_mode_graph()

# training
train = Trainer(m, clustering, num_step, optimizer, scheduler)
train.fit(data, projected_data, l1, l2)
train.analysis()

Sample from the distribution

We also proved a function to easily sample from the distribution, Opt_GMM_Mapper.sample(num_samples, Q). This function will return a list of networkx graphs.

# Sample 8 samples from optimized distribution
G_list = m.sample(8, train.scheme)

Help

Please send bugs, feature requests and comments to [email protected], or [email protected].