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Fig. 9 a The raw remainder signal after removing the two most singular values from I t).

Fig. 7 Comparison of original blood pressure signal and the result of removing the two most singular values from the SVD of the combined signal I t).

Apparently removing the two most singular values in the SVD approach can recover the blood pressure signal, with no specific prior knowledge of shape required.

Figure 7 shows more detail of just the blood pressure curve and the result of removing the two most singular values, otherwise the same case as in Fig. 5. Figure 8 shows a closeup view of the blood pressure signal over one period, superposed with the combined I t) signal and the result of removing the two most singular values from that signal.

In fact, we discovered that it is possible to recover curves that look just like the original blood pressure data, by first rectifying and then smoothing the residual signal obtained after removing the two most singular values.

Removing the two most singular values from the composite signal I t), then rectifying and smoothing, gives a filtered signal that looks very like the desired blood pressure curve and will give correct heartrate values.

This new M matrix then gives a time series that should represent or capture the notches in I t). Figure 5 shows the blood pressure data, the gait data, the composite signal I t), the result (the residual) of removing just the most singular value from the time series by setting the first singular value in S to zero, and the result of also removing the second most singular value from I t).

We then perform a singular vector decomposition of the matrix, and enforce rank on by choosing only most significant singular values.

Selecting the first few basis vectors corresponding to the most significant singular values, the 3-D CIT is formulated as a weighted least squares estimation problem of the basis coefficients.

The highlighted are the coordinates of six characteristic real cubical functions (undef. are undefined, most frequently singular values ± ∞, while 0 are the zeros of the HC k, n,r) function).

The first and by far most dominant singular value (119.2), corresponds to a tissue-independent eigen-exon, while the following five eigen-exons, denoted E1,…, E5, are shown in Figure 3B.