Algorithm inclusion

Comparison of the measurements with the microdensitometers and the algorithms of calculation inclusive the filter function and the accuracy of measurement of all project partners. 

It is also worth noting that the stochastic optimization methods described previously are readily adapted to the inclusion of constraints. For example, in simulated annealing, if a move suggested at random takes the solution outside of the feasible region, then the algorithm can be constrained to prevent this by simply setting the probability of that move to 0. 

Fig. 8. Reconstruction of Young s modulus map in a simulated object. A 3D breast phantom was first designed in silico from MR anatomical images. Then a given 3D Young s modulus distribution was supposed with a 1 cm diameter stiff inclusion of 200 kPa (A). The forward problem was the computing of the 3D-displacement field using the partial differential equation [Eq. (5)]. The efficiency of the 3D reconstruction (inverse problem) of the mechanical properties from the 3D strain data corrupted with 15% added noise can be assessed in (B). The stiff inclusion is detected by the reconstruction algorithm, but its calculated Young s modulus is about 130 kPa instead of 200 kPa. From Ref. 44, reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.

This algorithm has many aspects similar to Iterative Target Transform Factor Analysis, ITTFA, as discussed in Chapter 5.2.2, and Alternating Least-Squares, ALS as introduced later in Chapter 5.4. The main difference is the inclusion of the window information as provided by the EFA plots. 

In practice, it often turns out that a significant number of variables can be deleted due to the above criteria, or that some variables are considered as a must for inclusion in a variable subset. This can speed up other algorithms for variable selection considerably. 

On the basis of these clustering results, the EPA library of FTIR spectra was Judged adequate as a source of spectra to form the data base for the mixture analysis problem and the dot product was deemed an adequate similarity measure. Every chemical class considered to be a candidate for Inclusion was subjected to the clustering algorithm. Only those classes exhibiting a high degree of Internal similarity were retained In the mixture analysis data base. 

One reason for the inclusion of a large number of variables is tliat typical analytical chemistry data do not obey some of the assumptions of the statistical methods used in variable selection (Martens and Naes, 1989). The results from these algorithms can therefore only be used as a guide and should not be... 

As was discussed in Section 3, the multiobjective framework of the proposed algorithm allows us to incorporate additional constraints in the selection problem. In this section, we have addressed two such constraints, namely the experimental resources constraint and the exclusion/inclusion constraint. 

Note that MATLAB s fzero algorithm stops after 35 iterations when it is about 2.7% away from the true root 2 with an approximate start at 1.5. From the inclusion interval [1.91, 2.1] it also ends rather prematurely and off target as well. 

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