Constrained Fourier estimation of short-term time-series gene expression data reduces noise and improves clustering and gene regulatory network predictions

Table 1 Comparison of mean correlation coefficients \(\rho\) between noisy gene profiles and de-noised gene profiles using ImulseDE or our constrained Fourier approximation

	All time points			“High noise” time points
	Noisy data	ImpulseDE	Constrained Fourier	Noisy data	ImpulseDE	Constrained Fourier
Cluster 1	0.97	0.99	0.99	0.68	0.82	0.91
Cluster 1	\((\pm 0.02)\)	\((\pm 0.02)\)	\((\pm 0.01)\)	\((\pm 0.22)\)	\((\pm 0.22)\)	\((\pm 0.18)\)
Cluster 2	0.94	0.98	0.99	0.73	0.90	0.97
Cluster 2	\((\pm 0.04)\)	\((\pm 0.02)\)	\((\pm 0.02)\)	\((\pm 0.17)\)	\((\pm 0.13)\)	\((\pm 0.08)\)
Cluster 3	0.97	0.99	1.00	0.80	0.95	0.99
Cluster 3	\((\pm 0.03)\)	\((\pm 0.01)\)	\((\pm 0.00)\)	\((\pm 0.16)\)	\((\pm 0.05)\)	\((\pm 0.01)\)
Cluster 4	0.97	0.65	0.96	0.79	0.32	0.90
Cluster 4	\((\pm 0.03)\)	\((\pm 0.03)\)	\((\pm 0.01)\)	\((\pm 0.19)\)	\((\pm 0.13)\)	\((\pm 0.05)\)
Cluster 5	0.93	0.98	0.99	0.58	0.82	0.91
Cluster 5	\((\pm 0.04)\)	\((\pm 0.02)\)	\((\pm 0.01)\)	\((\pm 0.19)\)	\((\pm 0.12)\)	\((\pm 0.08)\)
Cluster 6	0.98	0.99	0.95	0.92	0.96	0.98
Cluster 6	\((\pm 0.02)\)	\((\pm 0.01)\)	\((\pm 0.00)\)	\((\pm 0.10)\)	\((\pm 0.05)\)	\((\pm 0.03)\)

ISSN: 1471-2105