yobx.sklearn.decomposition.kernel_pca#

yobx.sklearn.decomposition.kernel_pca.sklearn_kernel_pca(g: GraphBuilderExtendedProtocol, sts: Dict, outputs: List[str], estimator: KernelPCA, X: str, name: str = 'kernel_pca') → str[source]#

Converts a sklearn.decomposition.KernelPCA into ONNX.

The out-of-sample transform replicates sklearn.decomposition.KernelPCA.transform():

Compute the pairwise kernel matrix between X (shape (N, F)) and the training data X_fit_ (shape (M, F)):
- linear — K = X @ X_fit_.T
- rbf — K[i,j] = exp(−γ · ||X[i] − X_fit_[j]||²)
- laplacian — K[i,j] = exp(−γ · ||X[i] − X_fit_[j]||₁) (not supported; raises NotImplementedError )
- poly — K = (γ · X @ X_fit_.T + coef0) ^ degree
- sigmoid — K = tanh(γ · X @ X_fit_.T + coef0)
- cosine — K[i,j] = (X[i]/‖X[i]‖) · (X_fit_[j]/‖X_fit_[j]‖)
- precomputed / callable — not supported; raises NotImplementedError

Centre the kernel using the statistics stored in _centerer:

K_pred_cols = K.sum(axis=1, keepdims=True) / M
K_centered  = K − K_fit_rows_ − K_pred_cols + K_fit_all_

Compute scaled eigenvectors (zero-eigenvalue columns set to 0):

scaled_alphas[:, non_zeros] = eigenvectors_[:, non_zeros]
                              / sqrt(eigenvalues_[non_zeros])

Project:

result = K_centered @ scaled_alphas     # (N, n_components)

The full ONNX graph (rbf example) is:

X (N, F)
  │
  └── ||X[i] − X_fit_[j]||² ────────────────────────────► sq_dists (N, M)
                                                                  │
       sq_dists × (−γ) ──► neg_scaled ──Exp──► K (N, M)
       │
   K − K_fit_rows_ − K.sum(axis=1)/M + K_fit_all_ ──► K_c (N, M)
       │
   MatMul(scaled_alphas) ──► output (N, n_components)

Parameters:

g – the graph builder to add nodes to
sts – shapes defined by scikit-learn
estimator – a fitted KernelPCA
outputs – desired output names
X – input tensor name
name – prefix name for the added nodes

Returns:

output tensor name

Raises:

NotImplementedError – for kernel='precomputed', callable kernels, or kernel='laplacian'

yobx.sklearn.decomposition.kernel_pca#

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