Package: matrix-fact
MatrixFactInstallpip install matrix-factWhat is matrix-fact?matrix-fact contains modules for constrained/unconstrained matrix factorization (and related) methods for both sparse and dense matrices. The repository can be found athttps://github.com/gentaiscool/matrix_fact. The code is based onhttps://github.com/ChrisSchinnerl/pymf3andhttps://github.com/rikkhill/pymf. We updated the code to support the latest library. It requires cvxopt, numpy, scipy and torch. We just added the support for PyTorch-based SNMF.PackagesThe package includes:Non-negative matrix factorization (NMF) [three different optimizations used]Convex non-negative matrix factorization (CNMF)Semi non-negative matrix factorization (SNMF)Archetypal analysis (AA)Simplex volume maximization (SiVM) [and SiVM for CUR, GSAT, ... ]Convex-hull non-negative matrix factorization (CHNMF)Binary matrix factorization (BNMF)Singular value decomposition (SVD)Principal component analysis (PCA)K-means clustering (Kmeans)C-means clustering (Cmeans)CUR decomposition (CUR)Compaxt matrix decomposition (CMD)PyTorch SNMFUsageGiven a dataset, most factorization methods try to minimize the Frobenius norm|data - W*H|by finding a suitable set of basis vectorsWand coefficients H. The syntax for calling the various methods is quite similar. Usually, one has to submit a desired number of basis vectors and the maximum number of iterations. For example, applying NMF to a dataset data aiming at 2 basis vectors within 10 iterations works as follows:>>>importmatrix_fact>>>importnumpyasnp>>>data=np.array([[1.0,0.0,2.0],[0.0,1.0,1.0]])>>>nmf_mdl=matrix_fact.NMF(data,num_bases=2,niter=10)>>>nmf_mdl.initialization()>>>nmf_mdl.factorize()The basis vectors are now stored innmf_mdl.W, the coefficients innmf_mdl.H. To compute coefficients for an existing set of basis vectors simply copy W to nmf_mdl.W, and set compW to False:>>>data=np.array([[1.5],[1.2]])>>>W=np.array([[1.0,0.0],[0.0,1.0]])>>>nmf_mdl=matrix_fact.NMF(data,num_bases=2,niter=1,compW=False)>>>nmf_mdl.initialization()>>>nmf_mdl.W=W>>>nmf_mdl.factorize()By changing py_fact.NMF to e.g. py_fact.AA or py_fact.CNMF Archetypal Analysis or Convex-NMF can be applied. Some methods might allow other parameters, make sure to have a look at the corresponding>>>help(py_fact.AA)documentation. For example, CUR, CMD, and SVD are handled slightly differently, as they factorize into three submatrices which requires appropriate arguments for row and column sampling.For PyTorch-SNMF>>>data=torch.FloatTensor([[1.5],[1.2]])>>>nmf_mdl=matrix_fact.NMF(data,num_bases=2)>>>nmf_mdl.factorize(niter=1000)Very large datasetsFor handling larger datasets py_fact supports hdf5 via h5py. Usage is straight forward as h5py allows to map large numpy matrices to disk. Thus, instead of passing data as a np.array, you can simply send the corresponding hdf5 table. The following example shows how to apply py_fact to a random matrix that is entirely stored on disk. In this example the dataset does not have to fit into memory, the resulting low-rank factorsW,Hhave to.>>>importh5py>>>importnumpyasnp>>>importmatrix_fact>>>>>>file=h5py.File('myfile.hdf5','w')>>>file['dataset']=np.random.random((100,1000))>>>sivm_mdl=matrix_fact.SIVM(file['dataset'],num_bases=10)>>>sivm_mdl.factorize()If the low-rank matricesW,Halso do not fit into memory, they can be initialized as a h5py matrix.>>>importh5py>>>importnumpyasnp>>>importmatrix_fact>>>>>>file=h5py.File('myfile.hdf5','w')>>>file['dataset']=np.random.random((100,1000))>>>file['W']=np.random.random((100,10))>>>file['H']=np.random.random((10,1000))>>>sivm_mdl=matrix_fact.SIVM(file['dataset'],num_bases=10)>>>sivm_mdl.W=file['W']>>>sivm_mdl.H=file['H']>>>sivm_mdl.factorize()Please note that currently not all methods work well with hdf5. While they all accept hdf5 input matrices, they sometimes lead to very high memory consumption on intermediate computation steps. This is difficult to avoid unless we switch to a completely disk-based storage.