gdsvd

GDSVD is a package for computing SVD via gradient descent.

Example usage:

• Install via pip install gdsvd

• Import:

  from gdsvd.svd import gd_svd
  

• Memmap input data, recommended for large datasets

  U_true = np.memmap("datasets/ranklogn-exp-500_U.bin", dtype=np.float64, mode='r', shape=(500, 6))
  S_true = np.memmap("datasets/ranklogn-exp-500_S.bin", dtype=np.float64, mode='r', shape=(6,))
  Vt_true = np.memmap("datasets/ranklogn-exp-500_Vt.bin", dtype=np.float64, mode='r', shape=(6, 500))
  M = np.memmap("datasets/ranklogn-exp-500_M.bin", dtype=np.float64, mode='r', shape=(500, 500))
  

• Ensure that the arrays are contiguous

  U_true = np.ascontiguousarray(U_true)
  S_true = np.ascontiguousarray(S_true)
  Vt_true = np.ascontiguousarray(Vt_true)
  M = np.ascontiguousarray(M)
  

• To run the method normally:

  U,S,Vt = gd_svd(M)
  

• To run the method with convergence tracking written to conv_out.txt:

   U,S,Vt = gd_svd(M, record_conv = 'conv_out.txt', U_true = U_true, S_true = S_true, Vt_true = Vt_true)
  

gdsvd is implemented as Algorithm 4 in the reference paper.

Included in the package are gdsvd3 (Algorithm 3) and power-method (Algorithm 5), which is the GD method with alternate stopping and the power method, respectively.

Reference: k-SVD via gradient descent