A New Modified Histogram Matching Normalization for Time Series Microarray Analysis
Abstract
:1. Introduction
2. Methods
Algorithm for Modified Histogram Matching Normalization
- (1)
- First sort all data in the whole data matrix according to magnitude from low to high;
- (2)
- Partition this sorted dataset into bins (), each bin containing exactly N numbers;
- (3)
- Sort each column in the original unsorted data matrix according to magnitude from low to high. This results in an matrix S with elements , where each column contains the same elements as in the original unsorted data matrix but in an order where the smallest values are on top and largest at the bottom;
- (4)
- For and , scale all elements in the ith row of matrix S using the following scaling function f
- (5)
- Return each scaled element in each column back to their original unsorted positions within the columns.
3. Results
3.1. Effects on Correlation
3.2. Effects on Correlation on Real Data
3.3. Effects on Reverse-Engineering via ODEs
4. Conclusions
Acknowledgements
Author Contributions
Conflicts of Interest
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Appendix
Quantile normalization
- (1)
- First each column is ordered so that the smallest value comes to the top:
- (2)
- Then each value is replaced by the row mean. For example the row mean for the first row is .
- (3)
- Finally each element is returned to their original position:
Modified histogram matching normalization
- (2)
- Data is ordered and divided into bins: , and .
- (3)
- Instead of taking the row means, the scaling function f as defined in Section 2 is applied to each element. For example element andThis scaling results in the following matrix:
- (4)
- Finally the scaled elements are returned into their original positions:
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Astola, L.; Molenaar, J. A New Modified Histogram Matching Normalization for Time Series Microarray Analysis. Microarrays 2014, 3, 203-211. https://doi.org/10.3390/microarrays3030203
Astola L, Molenaar J. A New Modified Histogram Matching Normalization for Time Series Microarray Analysis. Microarrays. 2014; 3(3):203-211. https://doi.org/10.3390/microarrays3030203
Chicago/Turabian StyleAstola, Laura, and Jaap Molenaar. 2014. "A New Modified Histogram Matching Normalization for Time Series Microarray Analysis" Microarrays 3, no. 3: 203-211. https://doi.org/10.3390/microarrays3030203