PMC:4996402 / 34073-37779 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/4996402","sourcedb":"PMC","sourceid":"4996402","source_url":"https://www.ncbi.nlm.nih.gov/pmc/4996402","text":"5. Simulation Results\nIn this section, computer simulations are carried out to compare and evaluate the performance of major NCA algorithms. As discussed in Section 3, mNCA, gNCA, NCAr and gfNCA utilize the same estimation method as NCA. Additionally, PosNCA and nnNCA rely on the same framework, i.e., minimizing the Frobenius norm of C^TA, where C^ denotes the estimated left null space of the connectivity matrix A and estimating S via the least-squares method. Therefore, only the simulation results pertaining to NCA, FastNCA, ROBNCA, NINCA and PosNCA will be presented in this section.\nThe synthetic data widely used in [17,29,31,32] are tested. This spectroscopy data contain M=3 hemoglobin solutions obtained by mixing up N=7 pure hemoglobin components, and the absorption spectra consist of K = 300 experiment points, which are measured for wavelengths in the range of 380–700 nm [29]. The aforementioned algorithms are tested when the observed data are corrupted with different levels of Gaussian noise and when the observations contain both Gaussian noise and outliers. The normalized mean square error (NMSE) and the data fitting error (DFE), i.e., ||AS−X||F, are adopted herein to measure the estimation accuracy. The simulation results are averaged over 50 iterations. The algorithms are first simulated by varying the SNR from −10 dB–20 dB. The NMSE for matrices A and S and the DFE are illustrated in Figure 4 and Figure 5, respectively. In terms of the test against both noise and outliers, the outliers are manually added into the observations by modeling them as a Bernoulli process with probability 0.1. The simulation results with respect to NMSE and DFE are depicted in Figure 6 and Figure 7, respectively. Under 10 dB SNR, a comparison of the performance of NCA-based algorithms in both the noise case and noise + outliers case is shown in Table 1. These experiments are performed in MATLAB 7.12.0 with a 2.5-GHz Intel Core i5 processor, and the computation time stands for the average time to perform one iteration of simulation experiments.\nmicroarrays-04-00596-t001_Table 1 Table 1 Normalized mean square error (NMSE), data fitting error (DFE) and computation time for different algorithms under 10 dB SNR. NINCA, non-iterative NCA; ROBNCA, robust NCA; PosNCA, positive NCA. Furthermore, we also employ these algorithms to quantitatively analyze a real dataset. In particular, a plant TRN in floral development using the Arabidopsis thaliana dataset housed in the Arabidopsis Gene Regulatory Information Server (AGRIS) [37] is analyzed. The initial dataset consists of 10 TFs and 57 genes. However, only seven TFs, namely LFY, AG, SEP3, AP2, AGL15, HY and AP3/PI, and 55 genes were found to be compliant with the NCA framework [38]. The simulation results to reconstruct the aforementioned seven TFs are depicted in Figure 8. It can be seen that NCA, ROBNCA and NINCA almost obtain an identical estimate for SEP3, and they share a similar trend for the reconstruction of other TFs. On the other hand, with respect to the estimation of SEP3, the results obtained by FastNCA and PosNCA are different from those exhibited by NCA, ROBNCA and NINCA.\nFigure 4 NMSE for different algorithms with respect to SNR from −10 dB–20 dB.\nFigure 5 Data fitting error for different algorithms with respect to SNR from −10 dB–20 dB.\nFigure 6 NMSE for different algorithms with respect to SNR from −10 dB–20 dB and outliers with probability 0.1.\nFigure 7 Data fitting error for different algorithms with respect to SNR from −10 dB–20 dB and outliers with probability 0.1.\nFigure 8 TFA reconstruction: estimation of seven TFAs of the Arabidopsis Gene Regulatory Information Server (AGRIS).\n\n6","divisions":[{"label":"Title","span":{"begin":0,"end":21}},{"label":"Table caption","span":{"begin":2066,"end":2303}},{"label":"Figure caption","span":{"begin":3174,"end":3254}},{"label":"Figure caption","span":{"begin":3253,"end":3347}},{"label":"Figure caption","span":{"begin":3346,"end":3460}},{"label":"Figure caption","span":{"begin":3459,"end":3587}},{"label":"Figure caption","span":{"begin":3586,"end":3705}}],"tracks":[{"project":"2_test","denotations":[{"id":"27600242-14673099-69476470","span":{"begin":627,"end":629},"obj":"14673099"},{"id":"27600242-23940252-69476471","span":{"begin":630,"end":632},"obj":"23940252"},{"id":"27600242-18400771-69476472","span":{"begin":633,"end":635},"obj":"18400771"},{"id":"27600242-22641712-69476473","span":{"begin":636,"end":638},"obj":"22641712"},{"id":"27600242-23940252-69476474","span":{"begin":890,"end":892},"obj":"23940252"},{"id":"27600242-16524982-69476475","span":{"begin":2549,"end":2551},"obj":"16524982"},{"id":"27600242-24228871-69476476","span":{"begin":2757,"end":2759},"obj":"24228871"}],"attributes":[{"subj":"27600242-14673099-69476470","pred":"source","obj":"2_test"},{"subj":"27600242-23940252-69476471","pred":"source","obj":"2_test"},{"subj":"27600242-18400771-69476472","pred":"source","obj":"2_test"},{"subj":"27600242-22641712-69476473","pred":"source","obj":"2_test"},{"subj":"27600242-23940252-69476474","pred":"source","obj":"2_test"},{"subj":"27600242-16524982-69476475","pred":"source","obj":"2_test"},{"subj":"27600242-24228871-69476476","pred":"source","obj":"2_test"}]}],"config":{"attribute types":[{"pred":"source","value type":"selection","values":[{"id":"2_test","color":"#93ece6","default":true}]}]}}