4. A Big Lie About Optimization Criterion of Lin & Tang

The correlation optimization criterion is one of the core components of the direct construction of weak correlation design (NOLH). It is one of the most important techniques for the successful construction of zero-correlation and weak correlations designs. C.D.Lin's OLHD-NOLH construct progrem actually uses mcc, but she lies multiple times.

Lin (2009) defines an optimization criterion max: "'max' is maximum absolute correlation", What is “maximum absolute correlation”？ Lin(2010) said， “Near orthogonality can be measured by the maximum correlation ρ_M(D)= max_i,j|ρ_ij(D)|”. However， in where, the search range of the max function is the absolute value of all elements of the correlation matrix. The element with the largest absolute value in the correlation matrix must be on the main diagonal and its value is 1. So，‘max’≡1, which completely loses the point of measuring correlation. The reason is that she removed the core condition "non-main diagonal element" of mcc. The author is not ignorant of this truth, Lin (2009) p.2 uses "off-diagonal element". Deliberately poaching this core condition from mcc is to avoid being identical to mcc.

Lin (2008, 2010) once said that she used ρ_M(D) from Bingham (2009), which is another lie, Bingham, a collaborator and colleague of C.D.Lin, is another student of Boxing Tang. Lin (2008) using big space cites the results of their collaboration at length. Bingham (2009) and Lin (2009) were published in the same issue of Biometrika. Boxin Tang is the signed author of both papers. Two different definitions and symbols are used for the same concept. Dr. Lin copied Bingham's (2009) ρ_M N times just couldn't correctly copy the key symbol "<" between i and j of the function definition range. The submission date of Bingham (2009) is 8 months later than that of He (2009), and the upload date of the revised manuscript is 6 months later than that of He (2009). Bingham's ρ_M(D) is undoubtedly homologous to 'max'. C.D.Lin wants to whitewash through Bingham (2009), can it be whitewashed?

Lin (2008) stated that she did not use ρ_M, “We have tried to use ρ_M(D) as an optimality criterion for several cases in the adapted algorithm. However, the results are not so good as those from using ρ²(D).” This is a lie!

Both mcc and ρ²(D)can measure correlation. The mcc is the simplest in form, the programming is the easiest, the running speed is the fastest, and it can directly to calculate the correlation confidence probability P value, and weak correlation boundary can be determined. But ρ²(D) is the most complicated in form, programming is the most troublesome,and the computing speed is the slowest and the confidence probability P value cannot be calculated, and ”near” boundary can not be determined. According to my comparison, to execute the program under the same conditions, the computing time required for ρ²(D) is 2.4 times that of mcc. The size (n!) of the permutation set of the vector increases explosively with the increase of n is an astronomical number, and it is very difficult to solve， and cannot be related with the critical value, The two-level search loop limit of Lin's constructor is fixed at 3000, and the total loop volume is 9×10⁶. Even if n=21, the Lin algorithm requires more than 220 times the time of the He algorithm. If a running of He(2009) takes 10 minutes, then Lin-algorithm takes 37 hours, and the confidence probability of correlation cannot be reported. Constructing NOLH(22,21) is more than 22 times longer. The actual running program of C.D.Lin is unlikely to use such an algorithm.

On the validity of judgments, we use an example which come from Table 1 of Lin(2010) to illustrate. The first 12 columns of the design are an OLHD constructed by Steinberge at al.(2006), and we abbreviate as S-L matrix below. The rightmost 4 columns of the design are supplemented by C.D.Lin. We show its P matrix in the figure 4.1.

The P values of the four rightmost columns are caused by the four columns supplemented, whose p-values are all greater than 0.99 or even 1, and should not be added to the S-L matrix. However, the ρ²(D) of these four columns with the S-L matrix are 0.012821, 0.012822, 0.012802, 0.012802, respectively, and there is no reason to think that these four columns are not near orthogonal columns of the S-L matrix.

The ρ²(D) is not superior at all compared with mcc. Lin did not tell the truth in her papers.

There are three results in OLHD published by C.D.Lin (OLH(11,7), OLH(12,6), OLH(13,6)) with better performance, one orthogonal column more than my results on my laptop, And many results for n>16 have 1 column less than mine. C.D.Lin's NOLH results are almost the same as my 2005-2006 results and worse than my 2016 results. Why is the performance of OLHD and NOLH so different? Please publish the program implementation language, calculation program, running computers and operating record. I reckon her OLHD was run on a fancy computer at the SFU campus, NOLH was the result of running on a laptop, and by no means is her algorithm any advantage. Her algorithm is modeled after mine.