Simple n-fold cross-validation

Block-Term Tensor Regression (BTTR)

BTTR is a deflation-based method in which the maximally correlated representations of X and Y are extracted via ACE/ACCoS (Automatic Component Extraction / Automatic Correlated Component Selection) at each iteration. Therefore, BTTR inherits the advantages of the proposed ACE/ACCoS and does not require one to set the model parameters manually. This provides BTTR with an additional important property: the ability to model complex data in which the optimal Multilinear Rank (MTR) is not necessarily stable across sequential decompositions.

[1] Faes, Axel, Flavio Camarrone, and Marc M. Van Hulle. "Single finger trajectory prediction from intracranial brain activity using block-term tensor regression with fast and automatic component extraction." IEEE Transactions on Neural Networks and Learning Systems (2022).

	for snr in SNRs:
	for ratio in ratios:
	tmp_core_tensor_G, tmp_components_P = modified_pstd(full_tensor_C, core_tensor_G, components_P, snr, ratio)
	bic = calculateBIC(full_tensor_C, tmp_core_tensor_G, tmp_components_P)
	if not optimal_bic or bic < optimal_bic:
	optimal_bic = bic
	optimal = (snr, ratio)
	core_tensor_G_out, components_P_out = tmp_core_tensor_G, tmp_components_P

	def pruning(core_tensor_G, components_P, ratio):
	r"""
	At each iteration, the threshold :math:`\tau \in [0, 100]` is used to reject unnecessary components from the n-mode :math:`S^{(n)} = \{r { \| } 100 (1 - \frac{\sum_i{\mathbf{G}_{(n) (r, i)}}}{ \sum_{t,i}{\mathbf{G}_{(n) (t, i)}} }) \ge \tau\}`, :math:`\mathbf{P}^{(n)} = \mathbf{P}^{(n)} (:, S^{(n)})` and :math:`\mathbf{G}^{(n)} = \mathbf{G}^{(n)} (S^{(n)}, :)`.

	See the following reference for a full overview of the algorithm:

	Yokota, Tatsuya, and Andrzej Cichocki. "Multilinear tensor rank estimation via sparse tucker decomposition." In 2014 Joint 7th International Conference on Soft Computing and Intelligent Systems (SCIS) and 15th International Symposium on Advanced Intelligent Systems (ISIS), pp. 478-483. IEEE, 2014.

	Args:
	core_tensor_G (np.ndarray): Core tensor obtained from the tucker decomposition of full_tensor_C
	components_P (np.ndarray): Factor matrices obtained from the tucker decomposition of full_tensor_C
	ratio (float/int): parameter for use in pruning of the components
	"""
	N = len(components_P)
	RR = [components_P[n].shape[1] for n in range(0, N)]
	components_P_out = [None] * N
	for n in range(0, N):
	Gm = tl.unfold(core_tensor_G, n)
	gm = tl.sum(tl.abs(Gm), 1)
	ids = [k for k in range(0, Gm.shape[0]) if ((1 - gm[k] / tl.sum(gm)) * 100) > ratio]
	inv_ids = [k for k in range(0, Gm.shape[0]) if k not in ids]
	RR[n] = len(inv_ids)

	Gm = Gm[inv_ids,:]
	components_P_out[n] = components_P[n][:,inv_ids]
	core_tensor_G = tl.fold(Gm, n, RR)
	return core_tensor_G, components_P_out

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