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NMTF

Non-Negative Matrix and Tensor Factorizations

Developped in collaboration with Advestis (Github)

NMF Example

from adnmtf import NMF
import numpy as np

w = np.array([[1, 2],
              [3, 4],
              [5, 6],
              [7, 8],
              [9, 10],
              [11, 12]])

h = np.array([[0.1, 0.2, 0.3, 0.4, 0.5, 0.6],
              [0.9, 0.8, 0.7, 0.6, 0.5, 0.4]])
m0 = w.dot(h)
my_nmfmodel = NMF(n_components=2)
estimator_ = my_nmfmodel.fit_transform(m0)
estimator_ = my_nmfmodel.predict(estimator_)

In this example, the matrix to be factorized is generated by the dot product of:

• NMF instantiates a NMF class with 2 components.
• fit_transform calls the functions below in the given order:
  • nmtf_base module: non_negative_factorization, nmf_init, r_ntf_solve
  • nmtf_core module: ntf_solve, ntf_solve_simple, ntf_update
• predict derives from fit_transform outputs ordered sample and feature indexes for future use in ordered heatmaps. predict calls nmf_predict and build_clusters in the nmtf_base module

NTF Example

from adnmtf import NTF
import pandas as pd

DATA_PATH = ...

df = pd.read_csv(DATA_PATH)
m0 = df.values
n_blocks = 5
my_ntfmodel = NTF(n_components=5)
estimator_ = my_ntfmodel.fit_transform(m0, n_blocks)
estimator_ = my_ntfmodel.predict(estimator_)

In this example, the tensor to be factorized is read in file data_ntf.csv. The tensor has 5 layers in the 3rd dimension and is formatted as a table with 5 blocks concatenated horizontally.

• NTF instantiates a NTF class with 5 components.
• fit_transform calls the functions below in the given order:
  • nmtf_base module: non_negative_tensor_factorization, ntf_init, r_ntf_solve
  • nmtf_core module: ntf_solve, ntf_solve_simple, ntf_update
• predict derives from fit_transform outputs ordered sample and feature indexes for future use in ordered heatmaps. predict calls nmf_predict and build_clusters in the nmtf_base module

Articles

Peer-reviewed articles

• (researchgate) A Tale of Two Matrix Factorizations
• (researchgate) Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations
• (nature) Learning the parts of objects by non-negative matrix factorization

Blog articles

• (Medium) Using Non-negative matrix factorization to classify companies

• (offconvex) Tensor Methods in Machine Learning