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Cc analysis: Difference between revisions
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The purpose of cc_analysis is to find a representation in low-dimensional space (e.g. 2D, 3D, 4D) that displays the relations of data sets to each other. For this, the procedure needs the values of correlation coefficients (CCs) calculated between the data sets (e.g. crystallographic intensities, or pixels of images). (Not all theoretically possible pairwise CCs are needed, but of course, the more the better.) | The purpose of cc_analysis is to find a representation in low-dimensional space (e.g. 2D, 3D, 4D) that displays the relations of data sets to each other. For this, the procedure needs the values of correlation coefficients (CCs) calculated between the data sets (e.g. crystallographic intensities, or pixels of images). (Not all theoretically possible pairwise CCs are needed, but of course, the more the better.) | ||
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. | ||
As the result (the vectors) are in low-dimensional space, and the data sets | As the result (the vectors) are in low-dimensional space, and the data sets reside in high-dimensional space, the procedure may be considered as ''multidimensional scaling'' - there are other procedures in multidimensional scaling, but this particular one has first been described in [http://journals.iucr.org/d/issues/2017/04/00/rr5141/index.html Diederichs, Acta D (2017)]. Alternatively, we can think of the procedure as ''unsupervised learning'', because it "learns" from the given CCs, and predicts the unknown CCs - or rather, the relations of even those data sets that have nothing (crystallography: no reflections; imaging: no pixels) in common. | ||
== Properties of cc_analysis == | == Properties of cc_analysis == | ||