Approximate joint diagonalization #571
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Really excited to have this in TensorLy @aarmey, it's a neat method! |
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| def jointdiag( | ||
| X, |
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I'd name this matrices or matrices_tensor - X makes me think it's a single matrix at first glance (though granted should read the docstring).
tensorly/utils/jointdiag.py
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| print(f"Sweep # 0: e = {e:.3e}") | ||
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| # Additional output parameters | ||
| Q_total = tl.eye(D) |
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Same for these intermediate variables: it would be helpful to give them intuitive names
| for k in range(max_iter): | ||
| # loop over all pairs of slices | ||
| for p, q in combinations(range(D), 2): | ||
| # Finds matrix slice with greatest variability among diagonal elements |
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Should we just refer to them as matrices rather than matrix slice everywhere when we talk of an element X[:, :, j] ?
| + tl.norm(Xh[all_but_pq, p]) ** 2 | ||
| + tl.norm(Xh[all_but_pq, q]) ** 2 | ||
| ) | ||
| xih = Xh[p, q] - Xh[q, p] |
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Same here, the name isn't super helpful
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| T. Fu and X. Gao, “Simultaneous diagonalization with similarity transformation for | ||
| non-defective matrices”, in Proc. IEEE International Conference on Acoustics, Speech | ||
| and Signal Processing (ICASSP 2006), vol. IV, pp. 1137-1140, Toulouse, France, May 2006. |
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Can we make it as a proper reference [1]_ and add it a reference section of the doctoring (see e.g.
tensorly/tensorly/decomposition/_cp.py
Line 681 in d4652c8
| for i in range(k): | ||
| temp_diag = np.diag(rng.randn(d)) | ||
| diags[:, :, i] = temp_diag | ||
| synthetic[:, :, i] = np.linalg.inv(mixing) @ temp_diag @ mixing |
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This is actually quite useful to understand the type of mixing allowed: might be useful to have a short Notes section in the doctoring to explain what kind of scrambling the algorithm supports and roughly what it does?
This adds a function for deriving an approximate joint diagonalization for a set of matrices. This function is the basis of solvers that derive PARAFAC factorization by diagonalizing the Tucker decomposition. By using only a few iterations, this can also be used to improve the starting estimate for initializing PARAFAC.