Classification using Discriminant Analysis

We can use the approach described in Linear Discriminant Analysis to classify all the X vectors in the training set for Example 1 of Linear Discriminant Analysis. This is shown on the left side of Figure 1 (only 16 of the 32 vectors are shown). As you can see, the first 6 vectors are classified correctly, while the 7^th (row 10) is not, since the true value is loam (cell R10), while the discriminant analysis predicts this vector to be in the sandy category (cell Z10).

Figure 1 – Classification Table

We can then create a classification table (aka a confusion table) as shown in range AB3:AG8. E.g. cell AC4 contains the formula

=COUNTIFS($R$4:$R$35,$AB4,$Z$4:$Z$35,AC$3)

Highlighting range AC4:AF7 and pressing Ctrl-R and Ctrl-D fills in the other cells, with the marginal totals being added in an obvious way.

Using the classification table, we can also calculate a table of misclassifications as shown in range AB12:AF17. E.g. range AC13:AC16 contains the array formula =DIAG(AC4:AF7). We see that 75% of the vectors in the loam population are correctly classified by the model, while overall 56.3% of the vectors are correctly classified.

Reference

Penn State (2017) Estimating misclassification probabilities. STAT 505 Applied Multivariate Statistical Analysis
https://online.stat.psu.edu/stat505/lesson/10/10.5