Chapter Questions
The feature vectors of three classes are given. Using the 3-nearest neighbors classifier, classify the test vector $\{16,16\}$.$$\begin{array}{l|l|l}\hline \text { Class } & \text { Feature 1 } & \text { Feature 2 } \\\hline \text { Class1 } & 14 & 16 \\\hline \text { Class1 } & 14 & 14 \\\hline \text { Class1 } & 13 & 17 \\\hline \text { Class2 } & 18 & 14 \\\hline \text { Class2 } & 17 & 16 \\\hline \text { Class2 } & 17 & 15 \\\hline \text { Class3 } & 14 & 17 \\\hline \text { Class3 } & 17 & 19 \\\hline \text { Class3 } & 15 & 17 \\\hline\end{array}$$
The feature vectors of three classes are given. Using the 3-nearest neighbors classifier, classify the test vector $\{16,17\}$.$$\begin{array}{l|l|l}\hline \text { Class } & \text { Feature 1 } & \text { Feature 2 } \\\hline \text { Class1 } & 15 & 16 \\\hline \text { Class1 } & 16 & 19 \\\hline \text { Class1 } & 15 & 17 \\\hline \text { Class2 } & 17 & 14 \\\hline \text { Class2 } & 18 & 15 \\\hline \text { Class2 } & 17 & 15 \\\hline \text { Class3 } & 14 & 17 \\\hline \text { Class3 } & 17 & 18 \\\hline \text { Class3 } & 14 & 16 \\\hline\end{array}$$
The feature vectors of three classes are given. Using the 3-nearest neighbors classifier, classify the test vector $\{17,16\}$.$$\begin{array}{l|l|l}\hline \text { Class } & \text { Feature 1 } & \text { Feature 2 } \\\hline \text { Class1 } & 15 & 17 \\\hline \text { Class1 } & 16 & 20 \\\hline \text { Class1 } & 14 & 14 \\\hline \text { Class2 } & 20 & 13 \\\hline \text { Class2 } & 17 & 14 \\\hline \text { Class2 } & 18 & 15 \\\hline \text { Class3 } & 16 & 16 \\\hline \text { Class3 } & 13 & 18 \\\hline \text { Class3 } & 16 & 19\end{array}$$
Let the mean feature vectors of three classes be $\{10,10\},\{-10,-10\}$, and $\{10,-10\}$. Let the test vectors be $\{12,-10\},\{8,9\}$, and $\{-9,-11\}$. Find the three discriminant functions of the three classes. Classify the test vectors.
Let the mean feature vectors of three classes be $\{22,-20\},\{20,20\}$, and $\{-18,-19\}$. Let the test vectors be $\{23,-20\},\{21,18\}$, and $\{-18,-19\}$. Find the three discriminant functions of the three classes. Classify the test vectors.
Let the mean feature vectors of three classes be $\{15,-17\},\{17,15\}$, and $\{-16,16\}$. Let the test vectors be $\{18,-16\},\{18,14\}$, and $\{-16,16\}$. Find the three discriminant functions of the three classes. Classify the test vectors.
Draw the decision tree flowchart for classifying the five objects.$$\begin{array}{l|l|l|l|l|l}\hline \text { Object } & \text { F } & \text { O } & \text { U } & \text { R } & \text { S } \\\hline \text { Area } & 750 & 964 & 647 & 1084 & 658 \\\hline \text { Form } & 132 & 484 & 108 & 233 & 116 \\\hline\end{array}$$
Draw the decision tree flowchart for classifying the five objects.$$\begin{array}{l|l|l|l|l|l}\hline \text { Object } & 5 & 6 & 7 & 8 & 9 \\\hline \text { Area } & 1199 & 1245 & 822 & 1478 & 1229 \\\hline \text { Form } & 168 & 327 & 205 & 445 & 327 \\\hline\end{array}$$
Draw the decision tree flowchart for classifying the five objects.$$\begin{array}{l|l|l|l|l|l}\hline \text { Object } & 0 & 1 & 2 & 3 & 4 \\\hline \text { Area } & 1419 & 880 & 1090 & 1023 & 1118 \\\hline \text { Form } & 576 & 273 & 183 & 176 & 402 \\\hline\end{array}$$
Samples of training data of two classes, $c 1(m, n)$ and $c 2(m, n)$, are$$c 1(m, n)=\left[\begin{array}{l}0.7124-1.0637 \\1.0219-1.3503 \\1.0487-0.6465 \\1.7837-0.5444 \\2.4486-0.3089 \\1.4430-0.6230 \\0.8010-0.9970 \\1.5931-1.0655\end{array}\right] \quad c 2(m, n)=\left[\begin{array}{rr}-1.2296 & 0.7281 \\-1.2066 & 0.6124 \\-1.7524 & 3.1638 \\1.3789 & 0.6478 \\-2.2385 & -0.5050 \\-1.6842 & 3.2676 \\-2.0069 & 2.7461 \\-2.6606 & 0.6753\end{array}\right]$$Classify the test samples $t(m, n)$ using Bayes classification.$$t(m, n)=\left[\begin{array}{rr}0.4804 & -1.2375 \\1.0979 & -0.8694 \\-1.7471 & 0.1364 \\-0.8781 & 0.2799 \\-0.9416 & 0.6194 \\-2.9676 & 1.2279\end{array}\right]$$with(i) $p\left(\omega_1\right)=0.9$ and $p\left(\omega_2\right)=0.1$.(ii) $p\left(\omega_1\right)=0.1$ and $p\left(\omega_2\right)=0.9$.
Samples of training data of two classes, $c 1(m, n)$ and $c 2(m, n)$, are$$c 1(m, n)=\left[\begin{array}{r}-1.3587-1.7484 \\1.5513-0.9966 \\-1.0799-1.7673 \\-1.2003-1.9427 \\1.0758-0.6775 \\0.1002-1.2125 \\1.3904-0.5126 \\1.6422-0.7607\end{array}\right] \quad c 2(m, n)=\left[\begin{array}{rr}-1.2082 & -0.4353 \\0.4252 & 0.3338 \\-4.0033 & 1.1938 \\-1.7136 & 0.5872 \\-2.7969 & 1.4268 \\-1.5411 & 1.5656 \\-0.0826 & -0.3152 \\0.1678 & 0.7499\end{array}\right]$$Classify the test samples $t(m, n)$ using Bayes classification.$$t(m, n)=\left[\begin{array}{rr}-2.5374 & -2.4336 \\1.7707 & -0.8282 \\-1.7326 & 2.1029 \\-3.5297 & 1.9491 \\-1.3760 & -0.9096 \\-2.2018 & 1.1494\end{array}\right]$$with$p\left(\omega_1\right)=0.5$ and $p\left(\omega_2\right)=0.5$.
Samples of training data of two classes, $c 1(m, n)$ and $c 2(m, n)$, are$$\begin{aligned}& c 1(m, n)=\left[\begin{array}{l}2.6140-0.5545 \\0.5164-1.0168 \\0.9973-1.4846 \\1.8727-0.5267 \\1.1421-0.6542 \\2.3328-0.3331 \\1.9811-0.2564 \\1.2766-0.1643\end{array}\right] \\& c 2(m, n)=\left[\begin{array}{rr}0.3066 & 1.8237 \\-0.6225 & -0.4234 \\-0.0926 & 1.0912 \\-0.3983 & 1.8489 \\-2.8593 & -0.9255 \\-1.5889 & 1.4916 \\0.7320 & 0.7428 \\-1.0616 & -0.3287\end{array}\right] \\&\end{aligned}$$Classify the test samples $t(m, n)$ using Bayes classification.$$t(m, n)=\left[\begin{array}{rr}1.5646 & -1.3982 \\0.2250 & -1.5204 \\-1.8283 & -1.3793 \\-2.0365 & 0.0497 \\-2.6668 & 0.3246 \\-0.3692 & 0.8388\end{array}\right]$$with$p\left(\omega_1\right)=0.4$ and $p\left(\omega_2\right)=0.6$.