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PCA Sync Task

The Principal Component Analysis (PCA) sync task projects complex data onto a reduced set of orthogonal modes. Given an input tensor \(X \in \mathbb{C}^{F \times H \times W}\), the task reshapes it into a sample matrix \(X_{(N \times F)}\) with \(N = H \cdot W\), forms the Hermitian covariance

\[ C = X^\mathrm{H} X, \]

computes the eigenpairs associated with indices begin (inclusive) through end (exclusive), and finally produces the principal component responses

\[ Y = X \, V_{[\text{begin}:\text{end}]}, \]

where the columns of \(V\) are the selected eigenvectors.

Warning

The input is not mean-centered before decomposition.

Note

Eigenvalues are returned in ascending order. To capture the most energetic components, choose indices close to F (for example, begin = F - K, end = F to keep the K largest modes).

Inputs

This task has a single input of shape (F, H, W), where:

  • F: number of features (e.g., frames or spectral slices)
  • H: height (rows)
  • W: width (columns)

The dtype must be complex 32-bit (complex32) and the tensor must reside in device memory.

Outputs

This task produces a single output of shape ((end - begin), H, W), where:

  • end - begin: number of retained principal components
  • H: height (same as input)
  • W: width (same as input)

The dtype of the output tensor is complex 32-bit (complex32) and it is written to device memory.

Inplace

This task does not support inplace operation.

Ownership

This task does not own any inputs or outputs.

Settings

Example:

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{
    "begin": 0,
    "end": 8
}
Property Pattern Type Deprecated Definition Title/Description
+ begin No integer No - Inclusive index of the first eigencomponent to keep. Must satisfy:
- begin >= 0
- begin < end
+ end No integer No - Exclusive index of the last eigencomponent to keep. Must satisfy:
- end > begin
- end <= number of input features