A Python implementation of R-PCA using principle component pursuit by alternating directions. The theory and implementation of the algorithm is described here: http://statweb.stanford.edu/~candes/papers/RobustPCA.pdf
# generate low rank synthetic data
N = 100
num_groups = 3
num_values_per_group = 40
p_missing = 0.2
Ds = []
for k in range(num_groups):
d = np.ones((N, num_values_per_group)) * (k + 1) * 10
Ds.append(d)
D = np.hstack(Ds)
# decimate 20% of data
n1, n2 = D.shape
S = np.random.rand(n1, n2)
D[S < 0.2] = 0
# use R_pca to estimate the degraded data as L + S, where L is low rank, and S is sparse
rpca = R_pca(D)
L, S = rpca.fit(max_iter=10000, iter_print=100)
# visually inspect results (requires matplotlib)
rpca.plot_fit()
plt.show()