TY - JOUR
T1 - Erratum
T2 - Triclustering method for finding biomarkers in human immunodeficiency virus-1 gene expression data (Mathematical Biosciences and Engineering (2022) 19: 7 (6743-6763) DOI: 10.3934/mbe.2022318)
AU - Siswantining, Titin
AU - Bustamam, Alhadi
AU - Sarwinda, Devvi
AU - Soemartojo, Saskya Mary
AU - Latief, Moh Abdul
AU - Octaria, Elke Annisa
AU - Siregar, Anggrainy Togi Marito
AU - Septa, Oon
AU - Al-Ash, Herley Shaori
AU - Saputra, Noval
N1 - Publisher Copyright:
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
PY - 2023
Y1 - 2023
N2 - A correction on Triclustering method for finding biomarkers in human immunodeficiency virus-1 gene expression data by Titin Siswantining, Alhadi Bustamam, Devvi Sarwinda, Saskya Mary Soemartojo, Moh. Abdul Latief, Elke Annisa Octaria, Anggrainy Togi Marito Siregar, Oon Septa, Herley Shaori Al-Ash and Noval Saputra. Mathematical Biosciences and Engineering, 2022, 19(7):6743-6763. doi: 10.3934/mbe.2022318. We have updated Subsection 2.2.2 especially about Multi Slope Measure (MSL) in pages 6747-6749. We've added citations for this section [1], rewritten the sentences, and changed some of the equation notation (Eqs (2.9)-(2.12)). Then, we change notation in Figure 2 and added source for Figures 2 and 3. Understanding MSL requires a graphic representation of tricluster TRIxyz, where x, y, and z are one of gene G, condition C, and time or depth T so that element x on TRIxyz will be on the X-axis, and element y on TRIxyz will outline the panels that are elements z on TRIxyz as shown in Figure 2 [2]. MSL calculates the difference among the angles formed by every series traced on each of three representations, taking into account TRIgct, TRIgtc, and TRItgc on Figure 3. MSL accounts for the effect of adjacent points in time. MSL measures the average difference between the angles formed by the probe ID gene in all rows and columns for each individual or candidate tricluster. To calculate the MSL measure of a tricluster, a multiangular ratio calculation is first performed. Define the FGmulti tricluster TRItgc as the average difference ∆ from an angle vector avyz ∈ angset from all of the outlines y, for each panel p (Vmc), and the same for the rest of panels (Hmc), where Nmc is the number of differences that are formed. All the angular vectors of an outline y on panel z are defined as a set of angles formed by outline y, taking into account each data point on the X-axis. Each outline will have many (axis mark X-1) angles. The difference ∆ between two vector angles avA and avB is defined as the average of MAX - MIN (MAX is the maximum, and MIN is the minimum of the two angles avA(i) and avB(i)) of any component or angle i from avA and avB. (Equation presented) where: (Equation presented)FGmulti is based on multiple operations with the avyz angle vector. These elements are obtained based on the concept of a series, so the series Syz from the outline y for each panel z is the set of value pairs from the X-axis (xi) and expression level (elj), which forms the outline. For each set Syz, the angle of alpha axi is the spin arctangent of the slope of the line formed by the points (xi, eli) and (xnext(i), elnext(i)). The spin operation from an angle is the positive equivalent of the angle if it is negative. (Equation presented) spin(axi) = axi, if axi ≥ 0 and spin(axi = axi + (2 + π) if axi < 0 To conclude, the MSL measure of a TRI tricluster as shown in Eq (2.12) is the mean of the angular comparisons of three graphical representations of a tricluster. MSL(TRI) = 1/3[FGmulti(TRIgct) + FGmulti(TRIgtc) + FGmulti(TRItgc)] (2.12) In Section 2.5. Trigen Algorithm, we have rewritten the sentences for first and second paragraf, and changed some of the equations for pages 6753 and 6754. We also added citation for this section in [2]. Trigen algorithm is an algorithm based on the theory of evolution, genetic algorithm [1]. Genetic algorithm is an algorithm that aims to maximize a problem that will produce the best solution. Because in the Trigen algorithm we want to produce N-set triclusters, we need to do a genetic algorithm that is N-times. For the Trigen algorithm, MSL results are added to the genetic algorithm fitness function FF(TRI) along with the individul size and overlap control [2]. MSL combined with six other factors to be a weighted average. The first three factors is 1 - |TRIG|/DG, 1 - |TRIC|/DC|, and 1 - |TRIT|/DT | measure the number of genes, conditions, and time of TRI(TRIG,C,T) compared to the size of the dataset (|DG,C,T|). Because MSL minimizes the fitness function, therefore on these three factors are made 1- each proportion to produce a TRI with a larger size when the parameter wg, wc or wt is increased. The next three factors RG(TRI,SOL)/|TRIG|×|SOLL|, RC(TRI,SOL)/TRIC|×|SOLLand RT(TRI,SOL)/TRIT|×|SOLL) measure the number of genes, conditions, and time or depth elements TRI on the set of solutions that have been found previously SOL(|TRIG,C,T| × |SOL|) to produce TRI with a small overlap as the wag, wac, or wat value increases. Finally, the main function MSL(TRI)/2π measures the MSL(TRI) proportional value close to its maximum value of 2π to produce TRI with a small MSL value when the wf value is increased. The default total configuration value for wf, wg, wc, wt, wag, wac, wat is 1, with fix value for wf is 0.8 and the total others variables are 0.2. (Equation presented).
AB - A correction on Triclustering method for finding biomarkers in human immunodeficiency virus-1 gene expression data by Titin Siswantining, Alhadi Bustamam, Devvi Sarwinda, Saskya Mary Soemartojo, Moh. Abdul Latief, Elke Annisa Octaria, Anggrainy Togi Marito Siregar, Oon Septa, Herley Shaori Al-Ash and Noval Saputra. Mathematical Biosciences and Engineering, 2022, 19(7):6743-6763. doi: 10.3934/mbe.2022318. We have updated Subsection 2.2.2 especially about Multi Slope Measure (MSL) in pages 6747-6749. We've added citations for this section [1], rewritten the sentences, and changed some of the equation notation (Eqs (2.9)-(2.12)). Then, we change notation in Figure 2 and added source for Figures 2 and 3. Understanding MSL requires a graphic representation of tricluster TRIxyz, where x, y, and z are one of gene G, condition C, and time or depth T so that element x on TRIxyz will be on the X-axis, and element y on TRIxyz will outline the panels that are elements z on TRIxyz as shown in Figure 2 [2]. MSL calculates the difference among the angles formed by every series traced on each of three representations, taking into account TRIgct, TRIgtc, and TRItgc on Figure 3. MSL accounts for the effect of adjacent points in time. MSL measures the average difference between the angles formed by the probe ID gene in all rows and columns for each individual or candidate tricluster. To calculate the MSL measure of a tricluster, a multiangular ratio calculation is first performed. Define the FGmulti tricluster TRItgc as the average difference ∆ from an angle vector avyz ∈ angset from all of the outlines y, for each panel p (Vmc), and the same for the rest of panels (Hmc), where Nmc is the number of differences that are formed. All the angular vectors of an outline y on panel z are defined as a set of angles formed by outline y, taking into account each data point on the X-axis. Each outline will have many (axis mark X-1) angles. The difference ∆ between two vector angles avA and avB is defined as the average of MAX - MIN (MAX is the maximum, and MIN is the minimum of the two angles avA(i) and avB(i)) of any component or angle i from avA and avB. (Equation presented) where: (Equation presented)FGmulti is based on multiple operations with the avyz angle vector. These elements are obtained based on the concept of a series, so the series Syz from the outline y for each panel z is the set of value pairs from the X-axis (xi) and expression level (elj), which forms the outline. For each set Syz, the angle of alpha axi is the spin arctangent of the slope of the line formed by the points (xi, eli) and (xnext(i), elnext(i)). The spin operation from an angle is the positive equivalent of the angle if it is negative. (Equation presented) spin(axi) = axi, if axi ≥ 0 and spin(axi = axi + (2 + π) if axi < 0 To conclude, the MSL measure of a TRI tricluster as shown in Eq (2.12) is the mean of the angular comparisons of three graphical representations of a tricluster. MSL(TRI) = 1/3[FGmulti(TRIgct) + FGmulti(TRIgtc) + FGmulti(TRItgc)] (2.12) In Section 2.5. Trigen Algorithm, we have rewritten the sentences for first and second paragraf, and changed some of the equations for pages 6753 and 6754. We also added citation for this section in [2]. Trigen algorithm is an algorithm based on the theory of evolution, genetic algorithm [1]. Genetic algorithm is an algorithm that aims to maximize a problem that will produce the best solution. Because in the Trigen algorithm we want to produce N-set triclusters, we need to do a genetic algorithm that is N-times. For the Trigen algorithm, MSL results are added to the genetic algorithm fitness function FF(TRI) along with the individul size and overlap control [2]. MSL combined with six other factors to be a weighted average. The first three factors is 1 - |TRIG|/DG, 1 - |TRIC|/DC|, and 1 - |TRIT|/DT | measure the number of genes, conditions, and time of TRI(TRIG,C,T) compared to the size of the dataset (|DG,C,T|). Because MSL minimizes the fitness function, therefore on these three factors are made 1- each proportion to produce a TRI with a larger size when the parameter wg, wc or wt is increased. The next three factors RG(TRI,SOL)/|TRIG|×|SOLL|, RC(TRI,SOL)/TRIC|×|SOLLand RT(TRI,SOL)/TRIT|×|SOLL) measure the number of genes, conditions, and time or depth elements TRI on the set of solutions that have been found previously SOL(|TRIG,C,T| × |SOL|) to produce TRI with a small overlap as the wag, wac, or wat value increases. Finally, the main function MSL(TRI)/2π measures the MSL(TRI) proportional value close to its maximum value of 2π to produce TRI with a small MSL value when the wf value is increased. The default total configuration value for wf, wg, wc, wt, wag, wac, wat is 1, with fix value for wf is 0.8 and the total others variables are 0.2. (Equation presented).
UR - http://www.scopus.com/inward/record.url?scp=85149257716&partnerID=8YFLogxK
U2 - 10.3934/mbe.2023316
DO - 10.3934/mbe.2023316
M3 - Comment/debate
AN - SCOPUS:85149257716
SN - 1547-1063
VL - 20
SP - 7298
EP - 7301
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
IS - 4
ER -