def _Gauss_block_sparse_pre(self, x:np.array, y:np.array, K_ij:LazyTensor, sigma:float = 1., eps:float = 0.05): ''' Helper function to preprocess data for block-sparse reduction of the Gaussian kernel Args: x[np.array], y[np.array] = arrays giving rise to Gaussian kernel K(x,y) K_ij[LazyTensor_n] = symbolic representation of K(x,y) eps[float] = size for square bins Returns: K_ij[LazyTensor_n] = symbolic representation of K(x,y) with set sparse ranges ''' # class labels x_labels = grid_cluster(x, eps) y_labels = grid_cluster(y, eps) # compute one range and centroid per class x_ranges, x_centroids, _ = cluster_ranges_centroids(x, x_labels) y_ranges, y_centroids, _ = cluster_ranges_centroids(y, y_labels) # sort points x, x_labels = sort_clusters(x, x_labels) y, y_labels = sort_clusters(y, y_labels) # Compute a coarse Boolean mask: D = np.sum((x_centroids[:, None, :] - y_centroids[None, :, :]) ** 2, 2) keep = D < (4 * sigma) ** 2 # self.sigma # mask -> set of integer tensors ranges_ij = from_matrix(x_ranges, y_ranges, keep) K_ij.ranges = ranges_ij # block-sparsity pattern return K_ij
def _Gauss_block_sparse_pre(self, x: np.array, y: np.array, K_ij: LazyTensor): ''' Helper function to preprocess data for block-sparse reduction of the Gaussian kernel Args: x[np.array], y[np.array] = arrays giving rise to Gaussian kernel K(x,y) K_ij[LazyTensor_n] = symbolic representation of K(x,y) eps[float] = size for square bins Returns: K_ij[LazyTensor_n] = symbolic representation of K(x,y) with set sparse ranges ''' # labels for low dimensions if x.shape[1] < 4 or y.shape[1] < 4: x_labels = grid_cluster(x, self.eps) y_labels = grid_cluster(y, self.eps) # range and centroid per class x_ranges, x_centroids, _ = cluster_ranges_centroids(x, x_labels) y_ranges, y_centroids, _ = cluster_ranges_centroids(y, y_labels) else: # labels for higher dimensions x_labels, x_centroids = self._KMeans(x) y_labels, y_centroids = self._KMeans(y) # compute ranges x_ranges = cluster_ranges(x_labels) y_ranges = cluster_ranges(y_labels) # sort points x, x_labels = sort_clusters(x, x_labels) y, y_labels = sort_clusters(y, y_labels) # Compute a coarse Boolean mask: if self.kernel == 'rbf': D = np.sum((x_centroids[:, None, :] - y_centroids[None, :, :])**2, 2) elif self.kernel == 'exp': D = np.sqrt( np.sum((x_centroids[:, None, :] - y_centroids[None, :, :])**2, 2)) keep = D < (self.mask_radius)**2 # mask -> set of integer tensors ranges_ij = from_matrix(x_ranges, y_ranges, keep) K_ij.ranges = ranges_ij # block-sparsity pattern return K_ij