SUCCESSIVE NORMALIZATION OF RECTANGULAR ARRAYS.

Area of Science:

• Genomics
• Bioinformatics
• Financial Data Analysis
• Statistical Modeling

Background:

• Standard statistical methods often require data standardization (mean 0, standard deviation 1).
• High-throughput data, like genomic and financial datasets, are frequently structured as rectangular arrays.
• Existing standardization methods typically operate on subjects or features independently, not simultaneously.

Purpose of the Study:

• To address the need for simultaneous standardization of both subjects and features in rectangular data arrays.
• To propose and investigate a novel method for achieving "double normalization" across rows and columns.
• To evaluate the convergence and implementation of this successive normalization approach.

Main Methods:

• Development of a successive normalization algorithm for rectangular data matrices.
• Investigation of the convergence properties of the proposed double normalization method.
• Implementation and testing of the method on simulated and real-world scientific experimental data.

Main Results:

• The proposed successive normalization approach demonstrates convergence.
• Successful implementation of the double normalization technique on both simulated and experimental datasets.
• The method effectively standardizes subjects and features concurrently, placing them "on the same footing".

Conclusions:

• The developed double normalization method provides a viable solution for analyzing complex, high-throughput data.
• This approach enhances data comparability and analytical rigor in fields like genomics and finance.
• Further investigation into the application and refinement of this successive normalization technique is warranted.