Dynamic Fuzzy Machine Learning

For the original data, the minimum error criterion should be satisfied in the process of dimension reduction. Suppose the first a feature values are considered. The estimated value of the corresponding reconstruction is

$\overline{\left(\overleftarrow{X},\stackrel{\rightharpoonup }{X}\right)}={\displaystyle \sum _{i=1}^n\left({\overleftarrow{Y}}_i,{\stackrel{\rightharpoonup }{Y}}_i\right)\left({\overleftarrow{M}}_i,{\stackrel{\rightharpoonup }{M}}_i\right)\left(4.16\right)}$

The average variance is

$\left(e_a,e_a\right)=E\left[{\left(\left(\overleftarrow{X},\stackrel{\rightharpoonup }{X}\right)-\overline{\left(\overleftarrow{X},\stackrel{\rightharpoonup }{X}\right)}\right)}^2\right]={\displaystyle \sum _{l=a+1}^n\left({\overleftarrow{\lambda }}_i,{\stackrel{\rightharpoonup }{\lambda }}_i\right).\left(4.17\right)}$

When the a-eigenvalues of the $\left(\stackrel{\leftharpoonup }{X},\stackrel{\rightharpoonup }{X}\right)$ autocovariance matrix become larger, the mean square error becomes smaller. Thus, it is easy to find principal component whereby ...