I would like to cluster the data below with K-Means Clustering in Matlab. Table 11.9 on pages 666-667 contains data on breakfast cereals produced by three different American manufacturers: General Mills (G), Kellogg (K), and Quaker (Q). Assuming multivariate normal data with a common covariance matrix, equal costs, and equal priors, classify the cereal brands according to manufacturer. Compute the estimated E(AER) using the holdout procedure. Interpret the coefficients of the discriminant functions. Does it appear as if some manufacturers are associated with more "nutritional" cereals (high protein, low fat, high fiber, low sugar, and so forth) than others? Plot the cereals in the two-dimensional discriminant space, using different plotting symbols to identify the three manufacturers.

Table 11.9:

ACCheerios G 110 2 2 180 1.5 10.5 10 70 1 Cheerios G 110 6 2 290 2.0 17.0 1 105 1 CocoaPuffs G 110 1 1 180 0.0 12.0 13 55 1 CountChocula G 110 1 1 180 0.0 12.0 13 65 1 GoldenGrahams G 110 1 1 280 0.0 15.0 9 45 1 HoneyNutCheerios G 110 3 1 250 1.5 11.5 10 90 1 Kix G 110 2 1 260 0.0 21.0 3 40 1 LuckyCharms G 110 2 1 180 0.0 12.0 12 55 1 MultiGrainCheerios G 100 2 1 220 2.0 15.0 6 90 1 OatmealRaisinCrisp G 130 3 2 170 1.5 13.5 10 120 1 RaisinNutBran G 100 3 2 140 2.5 10..5 8 140 1 TotalCornFlakes G 110 2 1 200 0.0 21.0 3 35 1 TotalRaisinBran G 140 3 1 190 4.0 15.0 14 230 1 TotalWholeGrain G 100 3 1 200 3.0 16.0 3 110 1 Trix G 110 1 1 140 0.0 13.0 12 25 1 Cheaties G 100 3 1 200 3.0 17.0 3 110 1 WheatiesHoneyGold G 110 2 1 200 1.0 16.0 8 60 1 AllBran K 70 4 1 260 9.0 7.0 5 320 2 AppleJacks K 110 2 0 125 1.0 11.0 14 30 2 CornFlakes K 100 2 0 290 1.0 21.0 2 35 2 CornPops K 110 1 0 90 1.0 13.0 12 20 2 CracklinOatBran K 110 3 3 140 4.0 10.0 7 160 2 Crispix K 110 2 0 220 1.0 21.0 3 30 2 FrootLoops K 110 2 1 125 1.0 11.0 13 30 2 FrostedFlakes K 110 1 0 200 1.0 14.0 11 25 2 FrostedMiniWheats K 100 3 0 0 3.0 14.0 7 100 2 FruitfulBran K 120 3 0 240 5.0 14.0 12 190 2 JustRightCrunchyNuggets K 110 2 1 170 1.0 17.0 6 60 2 MueslixCrispyBlend K 160 3 2 150 3.0 17.0 13 160 2 NutNHoneyCrunch K 120 2 1 190 0.0 15.0 9 40 2 NutriGrainAlmondRaisin K 140 3 2 220 3.0 21.0 7 130 2 NutriGrainWheat K 90 3 0 170 3.0 18.0 2 90 2 Product19 K 100 3 0 320 1.0 20.0 3 45 2 RaisinBran K 120 3 1 210 5.0 14.0 12 240 2 RiceKrispies K 110 2 0 290 0.0 22.0 3 35 2 Smacks K 110 2 1 70 1.0 9.0 15 40 2 SpecialK K 110 6 0 230 1.0 16.0 3 55 2 CapNCrunch Q 120 1 2 220 0.0 12.0 12 35 3 HoneyGrahamOhs Q 120 1 2 220 1.0 12.0 11 45 3 Life Q 100 4 2 150 2.0 12.0 6 95 3 PuffedRice Q 50 1 0 0 0.0 13.0 0 15 3 PuffedWheat Q 50 2 0 0 1.0 10.0 0 50 3 QuakerOatmeal Q 100 5 2 0 2.7 1.0 1 110 3