BiFuncLib 0.0.6

A Python library for biclustering with functional data

BiFuncLib: A Python library for biclustering with functional data

BiFuncLib is a Python package that aggregates multiple biclustering methods.

Our package provides biclustering methods for both functional and scalar data (mainly for functional data). The functional-data approaches are further divided into biclustering and local clustering variants. A small set of scalar-data biclustering algorithms has also been included to ensure the package’s extensibility.

For functional data, in standard biclustering, each sample contains multiple functions, and the algorithm jointly clusters both samples and these functions across the entire dataset. In contrast, local clustering assumes only one function per sample; it segments that single function into local pieces and then performs biclustering on the resulting sub-functions.

Methods

This package is capable of handling a variety of biclustering methods, by category:

Functional data (biclustering)

• FunFEM (EM algorithm)
• FunLBM (Latent Block Model)
• FunCC (Cheng and Church)
• FunPF (Penalized Fusion)

Functional data (local clustering)

• FunSparse (Sparse clustering)
• FunSAS (Sparse And Smooth)
• FunLocal (Local clustering)

Scalar data

• Bimax (divide-and-conquer algorithm)
• SSVD (Sparse Singular Value Decomposition)
• CVX (ConVeX biclustering)

BiFuncLib unifies these approaches into a comprehensive and easily extensible biclustering toolkit. The framework is shown below.

We provide a web-based documentation which introduces the meaning of function parameters, the usage of functions, detailed information about methods, and gives examples for each. The web page is available at documentations. This package has been uploaded to PyPI with previous versions, and the web page is available at PyPI package. Users can also check releases to get historical versions.

Installation

It is recommended to use pip for installation:

pip install BiFuncLib

To get further information about installation and independencies, please move to installation instructions.

Quick Start

Below are individual usage examples for each method, including computational results and plots (where applicable).

FunFEM

fem_bifunc performs FunFEM algorithm which allows to cluster functional data by modeling the curves within a common and discriminative functional subspace.

import numpy as np
from BiFuncLib.fem_bifunc import fem_bifunc
from BiFuncLib.simulation_data import fem_sim_data
from BiFuncLib.BsplineFunc import BsplineFunc
from GENetLib.fda_func import create_fourier_basis
basis = create_fourier_basis((0, 181), nbasis=25)
time_grid = np.arange(1, 182).tolist()
fem_simdata = fem_sim_data()
fdobj = BsplineFunc(basis).smooth_basis(time_grid, np.array(fem_simdata['data'].T))['fd']
fem_res = fem_bifunc(fdobj, K=[6], model=['AkjBk'], init='kmeans', lambda_=0, disp=True)
FDPlot(fem_res).fem_fdplot(fem_simdata, fdobj)

FunLBM

lbm_bifunc performs FunLBM algorithm which is a model-based co-clustering method for large-scale functional data that simultaneously clusters rows and columns by fitting a latent block model where each block is represented by a low-dimensional functional subspace.

from BiFuncLib.simulation_data import lbm_sim_data
from BiFuncLib.lbm_bifunc import lbm_bifunc
from BiFuncLib.lbm_main_func import ari
lbm_simdata = lbm_sim_data(n = 100, p = 100, t = 30, seed = 1)
data = lbm_simdata['data']
lbm_res = lbm_bifunc(data, K=4, L=3)
FDPlot(lbm_res).lbm_fdplot('proportions')
print(ari(lbm_res['col_clust'],lbm_simdata['col_clust']))
print(ari(lbm_res['row_clust'],lbm_simdata['row_clust']))

FunCC

cc_bifunc performs FunCC, a non-parametric, non-exhaustive functional bi-clustering algorithm that extends the Cheng–Church framework; it simultaneously identifies row–column subsets of curves by minimizing an H-score and optionally aligns them with domain shifts, all without distributional assumptions.

cc_bifunc_cv provides a function for finding the best tunning delta.

import numpy as np
from BiFuncLib.simulation_data import cc_sim_data
from BiFuncLib.cc_bifunc import cc_bifunc, cc_bifunc_cv
delta_list = np.linspace(0.1, 20, num = 21)
fun_mat = cc_sim_data()
cc_result_cv = cc_bifunc_cv(fun_mat, delta_list = delta_list, alpha = 1, beta = 0, const_alpha = True)
cc_result = cc_bifunc(fun_mat, delta = 10, alpha = 1, beta = 0, const_alpha = True, shift_alignment = False)
FDPlot(cc_result).cc_fdplot(fun_mat, only_mean = True, aligned = False, warping = False)

FunPF

pf_bifunc performs FunPF, which is a penalized-fusion biclustering approach for functional data that combines a smoothness penalty for curve estimation with a fusion penalty on coefficient differences, enabling simultaneous and consistent identification of row and column clusters without assuming any generative model.

from BiFuncLib.pf_bifunc import pf_bifunc
from BiFuncLib.simulation_data import pf_sim_data
pf_simdata = pf_sim_data(n = 60, T = 10, nknots = 3, order = 3, seed = 123)['data']
pf_result = pf_bifunc(pf_simdata, nknots = 3, order = 3, gamma1 = 0.023, gamma2 = 3, 
                      theta = 1, tau = 3, max_iter = 500, eps_abs = 1e-3, eps_rel = 1e-3)
FDPlot(pf_result).pf_fdplot()

FunSparse

sparse_bifunc stands for FunSparse, an algorithm performs functional data grouping while simultaneously selecting the most discriminative curve regions via a hard-thresholded weighting function, yielding a concise and interpretable partition.

from BiFuncLib.simulation_data import sparse_sim_data
from BiFuncLib.sparse_bifunc import sparse_bifunc
K = 2
paramC = 0.7
n = 100
x = np.linspace(0, 1, 1000)
sparse_simdata = sparse_sim_data(n, x, paramC)['data']
part_vera = sparse_sim_data(n, x, paramC)['cluster']
sparse_res = sparse_bifunc(sparse_simdata, x, K, true_clus = part_vera)
FDPlot(sparse_res).sparse_fdplot(x, sparse_simdata)

FunSAS

sas_bifunc performs FunSAS algorithm. FunSAS simultaneously clusters functional curves and pinpoints, via adaptive pairwise-fusion penalized likelihood, the specific time intervals where each pair of cluster mean curves actually differ, thereby delivering both accurate grouping and a sparse, interpretable map of informative regions.

sas_bifunc_cv provides a function for finding the best tunning gamma.

from BiFuncLib.simulation_data import sas_sim_data
from BiFuncLib.sas_bifunc import sas_bifunc, sas_bifunc_cv
sas_simdata_0 = sas_sim_data(0, n_i = 20, var_e = 1, var_b = 0.25)
sas_result = sas_bifunc(X = sas_simdata_0['X'], grid = sas_simdata_0['grid'],
                        lambda_s = 1e-6, lambda_l = 10, G = 2, maxit = 5, q = 10)
lambda_s_seq = 10 ** np.arange(-4, -2, dtype=float)
lambda_l_seq = 10 ** np.arange(-1, 1, dtype=float)
G_seq = [2, 3]
sas_cv_result = sas_bifunc_cv(X = sas_simdata_0['X'], grid = sas_simdata_0['grid'],
                              lambda_l_seq = lambda_l_seq, lambda_s_seq = lambda_s_seq,
                              G_seq = G_seq, maxit = 20, K_fold = 2, q = 10)
FDPlot(sas_result).sas_fdplot()
FDPlot(sas_cv_result).sas_cvplot()

FunLocal

local_bifunc performs FunLocal, which simultaneously identifies data-driven subintervals and performs clustering within each, allowing functions to exhibit distinct grouping structures across different regions of their domain.

from BiFuncLib.local_bifunc import local_bifunc
from BiFuncLib.simulation_data import local_sim_data
local_simdata = local_sim_data(n = 100, T = 100, sigma = 0.75, seed = 1)
opt_res = local_bifunc(local_simdata['data'], local_simdata['location'],
                       1.02e-5, 2, 0.3, opt=False)
FDPlot(opt_res).local_individuals_fdplot()
FDPlot(opt_res).local_center_fdplot()

Bimax

bimax_biclus performs Bimax algorithm, which exhaustively finds all inclusion-maximal submatrices of 1s in a binarized data matrix without overlap.

from BiFuncLib.bimax_biclus import bimax_biclus
from BiFuncLib.simulation_data import bimax_sim_data
bimax_simdata = bimax_sim_data()
bimax_res = bimax_biclus(bimax_simdata, minr=4,minc=4,number=10)
bcheatmap(bimax_simdata,bimax_res)

SSVD

s4vd_biclus performs SSVD algorithm, which simultaneously sparsifies the left and right singular vectors of an SVD layer to extract coherent row–column blocks (biclusters).

Here, ssvd_biclus is the original algorithm, whereas s4vd_biclus is its cross-validated, hyper-parameter-tuned version; in practice, s4vd_biclus is recommended for modeling. The jaccardmat function is provided to measure similarity.

from BiFuncLib.simulation_data import ssvd_sim_data
from BiFuncLib.bcheatmap import bcheatmap
from BiFuncLib.ssvd_main_func import jaccardmat
from BiFuncLib.ssvd_biclus import s4vd_biclus, ssvd_biclus
ssvd_simdata = ssvd_sim_data()
data = ssvd_simdata['data']
res_sim = ssvd_simdata['res']
s4vd_res = s4vd_biclus(data, pcerv=0.5, pceru=0.5, pointwise=False, nbiclust=1)
print(jaccardmat(res_sim, s4vd_res, 'row'))
print(jaccardmat(res_sim, s4vd_res, 'column'))
bcheatmap(data, s4vd_res)
res2_ssvd = ssvd_biclus(data,K=1)
print(jaccardmat(res_sim, res2_ssvd))
bcheatmap(data, res2_ssvd)

CVX

cvx_biclus_valid performs COBRA algorithm with validation, which is a convex biclusteRing algorithm designed to identify checkerboard patterns in data matrices by solving a convex optimization problem, offering stability, uniqueness, and interpretability in biclustering.

cvx_biclus_missing handles data with missing values.

import numpy as np
import random
import math
from BiFuncLib.simulation_data import cvx_sim_data
from BiFuncLib.cvx_main_func import gkn_weights
from BiFuncLib.cvx_biclus import cvx_biclus_valid, cvx_biclus_missing
cvx_simdata = cvx_sim_data()
X = cvx_simdata.copy()
X = X - np.mean(np.mean(X))
X = X / np.linalg.norm(X, 'fro')
data = X
phi = 0.5
k = 5
# Example 1
wts = gkn_weights(X, phi=phi, k_row=k, k_col=k)
E_row = wts["E_row"]
E_col = wts["E_col"]
gam = 200
m_row = E_row.shape[0]
m_col = E_col.shape[0]
n = X.shape[1]
p = X.shape[0]
Lambda_row = np.random.randn(n, m_row)
Lambda_col = np.random.randn(p, m_col)
Theta = random.sample(range(1, n*p+1), math.floor(0.1 * n * p))
wts = gkn_weights(data, phi=phi, k_row=k, k_col=k)
w_row = wts["w_row"]
w_col = wts["w_col"]
E_row = wts["E_row"]
E_col = wts["E_col"]
cvx_res1 = cvx_biclus_missing(data, E_row, E_col, w_row, w_col, gam, Lambda_row, Lambda_col, Theta)
# Example 2
nGamma = 5
gammaSeq = 10 ** np.linspace(0, 3, nGamma)
wts = gkn_weights(data, phi=phi, k_row=k, k_col=k)
w_row = wts["w_row"]
w_col = wts["w_col"]
E_row = wts["E_row"]
E_col = wts["E_col"]
cvx_res2 = cvx_biclus_valid(data, E_row, E_col, w_row, w_col, gammaSeq, plot_error = False)

For more information about the functions and methods, please check main functions.

Reference

The main referenced papers of these methods are:

FunFEM

Bouveyron C, Côme E, Jacques J. The discriminative functional mixture model for the analysis of bike sharing systems[J]. Preprint HAL, 2014 (01024186).

FunLBM

Bouveyron C, Bozzi L, Jacques J, et al. The functional latent block model for the co-clustering of electricity consumption curves[J]. Journal of the Royal Statistical Society Series C: Applied Statistics, 2018, 67(4): 897-915.

FunCC

Galvani M, Torti A, Menafoglio A, et al. FunCC: A new bi-clustering algorithm for functional data with misalignment[J]. Computational Statistics & Data Analysis, 2021, 160: 107219.

FunPF

Fang K, Chen Y, Ma S, et al. Biclustering analysis of functionals via penalized fusion[J]. Journal of multivariate analysis, 2022, 189: 104874.

FunSparse

Floriello D, Vitelli V. Sparse clustering of functional data[J]. Journal of Multivariate Analysis, 2017, 154: 1-18.

FunSAS

Centofanti F, Lepore A, Palumbo B. Sparse and smooth functional data clustering[J]. Statistical Papers, 2024, 65(2): 795-825.

FunLocal

Chen Y, Zhang Q, Ma S. Local clustering for functional data[J]. Journal of Computational and Graphical Statistics, 2025: 1-16.

Bimax

Prelić A, Bleuler S, Zimmermann P, et al. A systematic comparison and evaluation of biclustering methods for gene expression data[J]. Bioinformatics, 2006, 22(9): 1122-1129.

SSVD

Lee M, Shen H, Huang J Z, et al. Biclustering via sparse singular value decomposition[J]. Biometrics, 2010, 66(4): 1087-1095.

CVX

Chi E C, Allen G I, Baraniuk R G. Convex biclustering[J]. Biometrics, 2017, 73(1): 10-19.

Other referenced papers can be obtained in references.

License

BiFuncLib is licensed under the MIT License. See LICENSE for details.

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