The Multi-View Latent BLock Model

An implementation of the Multi-View Latent Block Model (MVLBM) co-clustering method, presented in 'Co-Clustering Multi-View Data with the Latent Block Model'.

Dependencies

MVLBM supports Python 3, with numpy, scipy, scikit-learn and tqdm. These should be linked with a BLAS implementation (e.g., OpenBLAS, ATLAS, Intel MKL).

Installation

mvlbm is available on PyPI, the Python Package Index.

$ pip install mvlbm

How To Use

To use mvlbm, first import the MVLBM module.

    from mvlbm import mvlbm

Co-Clustering a Single-View Multi-Type Dataset

It is required to load in the Latent Block Model of the required data type.

#Continuous data
from mvlbm.gaussian_mixture import GaussianLatentBlockModel
#Ordinal data
from mvlbm.bos_mixture import BOSLatentBlockModel
#Binary data
from mvlbm.binomial_mixture import BinomialLatentBlockModel
#Nominal data
from mvlbm.multinomial_mixture import MultinomialLatentBlockModel
#Count data
from mvlbm.poisson_mixture import PoissonLatentBlockModel

If the dataset contains multiple types, the multi-set latent block model (mslbm) must be loaded.

#Multi-type data
from mvlbm.mslbm import MSLBM

The column indices denoting the variable sets are next specified.

col_indices = [np.arange(0, 10), np.arange(10, 20), np.arange(20, 30), np.arange(30, 40), np.arange(40, 50)]

Next specify the models for each variable set and define the MSLBM.

set_models = [GaussianLatentBlockModel(n_row_components = 2, n_col_components = 2),
                BOSLatentBlockModel(n_levels = 4, n_row_components = 2, n_col_components = 2),
                  BinomialLatentBlockModel(n_row_components = 2, n_col_components = 2),
                    MultinomialLatentBlockModel(n_levels = 5, n_row_components = 2, n_col_components = 2), 
                      PoissonLatentBlockModel(n_row_components = 2, n_col_components = 2)]
view_model = MSLBM(base_set_models = set_models, col_indices = col_indices)

To co-cluster a single-view dataset, we wrap the MSLBM model and apply it to the MVLBM in a list of length 1.

from mvlbm import MVLBM
view_data = [X]
view_models = [view_model]
model = MVLBM(base_view_models = view_models, max_n_steps = 150, burn_in_steps = 100, resampling_steps = 100, resampling_fraction = 0.2)
model.fit_sem(view_data)

MVLBM takes 6 arguments:

base_view_models The list of input models.
max_n_steps (Defaults to 150) The number of iterations of the SEM-Gibbs algorithm.
burn_in_steps (Defaults to 100) The number of iterations taken as burn-in (parameters estimated during this step are not combined to form final estimates).
resampling_steps (Defaults to 100) The number of steps for which resampling of empty clusters is completed.
resampling_fraction (Defaults to 0.2) The fraction of assignments to resample when empty clusters are found.

The MVLBM object is then fit to a dataset:

view_data A list of n-by-d_v numpy.ndarrays with training data. The rows correspond to n observations, and the columns correspond to d_v dimensions.

Testing for Association

Co-Clustering a Multi-View Dataset

It is required to load in the Latent Block Model of the required data type.

#Continuous data
from mvlbm.gaussian_mixture import GaussianLatentBlockModel
#Ordinal data
from mvlbm.bos_mixture import BOSLatentBlockModel
#Binary data
from mvlbm.binomial_mixture import BinomialLatentBlockModel
#Nominal data
from mvlbm.multinomial_mixture import MultinomialLatentBlockModel
#Count data
from mvlbm.poisson_mixture import PoissonLatentBlockModel

If the dataset contains multiple types, the multi-set latent block model (mslbm) must be loaded.

#Multi-type data
from mvlbm.mslbm import MSLBM

The column indices denoting the variable sets are next specified.

col_indices_0 = [np.arange(0, 10), np.arange(10, 20), np.arange(20, 30), np.arange(30, 40), np.arange(40, 50)]
col_indices_1 = [np.arange(0, 10), np.arange(10, 20), np.arange(20, 30), np.arange(30, 40), np.arange(40, 50)]

Next specify the models for each variable set and define the MSLBM for each view.

set_models_0 = [GaussianLatentBlockModel(n_row_components = 2, n_col_components = 2),
                BOSLatentBlockModel(n_levels = 4, n_row_components = 2, n_col_components = 2),
                  BinomialLatentBlockModel(n_row_components = 2, n_col_components = 2),
                    MultinomialLatentBlockModel(n_levels = 5, n_row_components = 2, n_col_components = 2), 
                      PoissonLatentBlockModel(n_row_components = 2, n_col_components = 2)]
view_model_0 = MSLBM(base_set_models = set_models_0, col_indices = col_indices_0)
set_models_1 = [GaussianLatentBlockModel(n_row_components = 2, n_col_components = 2),
                BOSLatentBlockModel(n_levels = 4, n_row_components = 2, n_col_components = 2),
                  BinomialLatentBlockModel(n_row_components = 2, n_col_components = 2),
                    MultinomialLatentBlockModel(n_levels = 5, n_row_components = 2, n_col_components = 2), 
                      PoissonLatentBlockModel(n_row_components = 2, n_col_components = 2)]
view_model_1 = MSLBM(base_set_models = set_models_1, col_indices = col_indices_1)

To co-cluster a multi-view dataset, we wrap the MSLBM model and apply it to the MVLBM in a list of length 1.

from mvlbm import MVLBM
view_data = [X0, X1]
view_models = [view_model_0, view_model_1]
model = MVLBM(base_view_models = view_models, max_n_steps = 150, burn_in_steps = 100, resampling_steps = 100, resampling_fraction = 0.2)
model.fit_sem(view_data)

MVLBM takes 6 arguments:

base_view_models The list of input models.
max_n_steps (Defaults to 150) The number of iterations of the SEM-Gibbs algorithm.
burn_in_steps (Defaults to 100) The number of iterations taken as burn-in (parameters estimated during this step are not combined to form final estimates).
resampling_steps (Defaults to 100) The number of steps for which resampling of empty clusters is completed.
resampling_fraction (Defaults to 0.2) The fraction of assignments to resample when empty clusters are found.

The MVLBM object is then fit to a dataset:

view_data A list of n-by-d_v numpy.ndarrays with training data. The rows correspond to n observations, and the columns correspond to d_v dimensions.

Experimentation

Simulated datasets can be created using the functions in the data_generator.py file. To simulate the datasets in the original paper:

python3 "Simulate Data.py"

MVLBM

mvlbm has an MIT License.

See LICENSE.

Funding

The AIM4HEALTH project gratefully acknowledges the support of the HEA, DFHERIS and the Shared Island Fund.

zshwuhan/MVLBM