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Cc analysis: Difference between revisions
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Since the data sets are composed of many measurements, they could be thought of as residing in a high-dimensional space: in case of crystallography, that dimension is the number of unique reflections; in case of images, the number of pixels. | Since the data sets are composed of many measurements, they could be thought of as residing in a high-dimensional space: in case of crystallography, that dimension is the number of unique reflections; in case of images, the number of pixels. | ||
If N is the number of data sets and <math>cc_{ij}</math> denotes the correlation coefficients between data sets i and j, cc_analysis minimizes | How is the low-dimensional representation found? If N is the number of data sets and <math>cc_{ij}</math> denotes the correlation coefficients between data sets i and j, cc_analysis minimizes | ||
<math>\Phi(\mathbf{x} )=\sum_{i=1}^{N-1}\sum_{j=i+1}^{N}\left(cc_{ij}-x_{i}\cdot x_{j}\right)^{2}</math> | <math>\Phi(\mathbf{x} )=\sum_{i=1}^{N-1}\sum_{j=i+1}^{N}\left(cc_{ij}-x_{i}\cdot x_{j}\right)^{2}</math> | ||