### Abstract

In independent component analysis (ICA), principal component analysis (PCA) is generally used to reduce the raw data to a few principal components (PCs) through eigenvector decomposition (EVD) on the data covariance matrix. Although this works for spatial ICA (sICA) on moderately sized fMRI data, it is intractable for temporal ICA (tICA), since typical fMRI data have a high spatial dimension, resulting in an unmanageable data covariance matrix. To solve this problem, two practical data reduction methods are presented in this paper. The first solution is to calculate the PCs of tICA from the PCs of sICA. This approach works well for moderately sized fMRI data; however, it is highly computationally intensive, even intractable, when the number of scans increases. The second solution proposed is to perform PCA decomposition via a cascade recursive least squared (CRLS) network, which provides a uniform data reduction solution for both sICA and tICA. Without the need to calculate the covariance matrix, CRLS extracts PCs directly from the raw data, and the PC extraction can be terminated after computing an arbitrary number of PCs without the need to estimate the whole set of PCs. Moreover, when the whole data set becomes too large to be loaded into the machine memory, CRLS-PCA can save data retrieval time by reading the data once, while the conventional PCA requires numerous data retrieval steps for both covariance matrix calculation and PC extractions. Real fMRI data were used to evaluate the PC extraction precision, computational expense, and memory usage of the presented methods.

Original language | English (US) |
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Pages (from-to) | 591-596 |

Number of pages | 6 |

Journal | Magnetic Resonance Imaging |

Volume | 24 |

Issue number | 5 |

DOIs | |

State | Published - Jun 1 2006 |

Externally published | Yes |

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### Keywords

- Cascade recursive least squared networks
- Independent component analysis
- Principal component analysis
- fMRI

### ASJC Scopus subject areas

- Biophysics
- Biomedical Engineering
- Radiology Nuclear Medicine and imaging

### Cite this

*Magnetic Resonance Imaging*,

*24*(5), 591-596. https://doi.org/10.1016/j.mri.2005.12.013