Fig. 2
Dissection iteration for a high-dimensional signal. A high-dimensional signature is detected and dissected from our versatility test scenario containing 13 superposed signatures and noise. a The input signal M0 is shown in the detected signature order. b Five overlapping signatures have already been detected and dissected in previous iterations. Their superposition depicts already explained parts of the signal. c Current signal Mk−1, displayed in the detected gene order Ik and sample order Jk. Sample strengths for each column (light brown) defining Jk were determined by projections of samples on the detected gene axis. Gene strengths for each row (light green) defining Ik were determined analogously. Samples sorted to the center are not affected by this signature and have strengths close to zero. d Specific contributions of the detected signature to the overall signal, as determined by regression according to our signature model. Consequently, these contributions are bi-monotonic in the displayed signature order (Ik, Jk). They are equivalent to a monotonic curve in the high-dimensional gene space. Gray shadings depict low gene and sample weights. (For a better overview, non-participating genes with weak strengths and low weights are hidden; their signature signal is close to zero.) e The residual signal Mk that remains after dissection of the regressed signature signal Ek is the input for the next detection iteration k + 1. Besides simulated noise, it still contains signals from seven superposed signatures with yet undetected random gene and sample orders.
