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Perform classification using the k-nearest neighbors algorithm with k-7 for the point (3, 10, 42) given in the table below. Find the TUMOR result. Example No 1 2 3 GEN1 10 9 7 3 5 2 6 11 7 7 8 4 9 1 New Example 3 45 4 GEN2 10 5 8 22 28 9 12 21 16 10 GEN3 44 42 25 65 56 32 21 61 10 42 TÜMÖR A A A BBAAB B B 2 ?

Perform classification using the k-nearest neighbors algorithm with k-7 for the point (3, 10, 42) given in the table below. Find the TUMOR result. Example No 1 2 3 GEN1 10 9 7 3 5 2 6 11 7 7 8 4 9 1 New Example 3 45 4 GEN2 10 5 8 22 28 9 12 21 16 10 GEN3 44 42 25 65 56 32 21 61 10 42 TÜMÖR A A A BBAAB B B 2 ?

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### Exercise in k-Nearest Neighbors Algorithm #### Problem Statement Perform classification using the k-nearest neighbors algorithm with \( k=7 \) for the point (3, 10, 42) given in the table below. Find the TUMOR result. #### Data Table | Example No | GEN1 | GEN2 | GEN3 | TUMOR | |------------|------|------|------|-------| | 1 | 10 | 10 | 44 | A | | 2 | 9 | 5 | 42 | A | | 3 | 7 | 8 | 25 | A | | 4 | 3 | 22 | 65 | B | | 5 | 2 | 28 | 56 | B | | 6 | 11 | 9 | 32 | A | | 7 | 7 | 12 | 21 | A | | 8 | 4 | 21 | 61 | B | | 9 | 1 | 16 | 10 | B | | New Example | 3 | 10 | 42 | ? | #### Explanation of the Method The k-nearest neighbors (k-NN) algorithm is a non-parametric method used for classification and regression. In both cases, the input consists of the \( k \) closest training examples in the feature space. The algorithm works on the principle that similar points can be found in close proximity. Key steps to apply the k-NN algorithm: 1. **Calculate the distance** between the new data point and all existing data points. 2. **Sort** the distances to identify the nearest neighbors. 3. **Determine the majority class** among these neighbors. 4. **Classify** the new data point based on the majority class. ##### Illustration Assuming the use of Euclidean distance, you would calculate the distance from the new example to each existing data point as follows: - Distance formula for Euclidean distance: \[ \text{distance} = \sqrt{(GEN1_{new} - GEN1_{i})^2 + (GEN2_{new} - GEN2_{i})^
Transcribed Image Text:### Exercise in k-Nearest Neighbors Algorithm #### Problem Statement Perform classification using the k-nearest neighbors algorithm with \( k=7 \) for the point (3, 10, 42) given in the table below. Find the TUMOR result. #### Data Table | Example No | GEN1 | GEN2 | GEN3 | TUMOR | |------------|------|------|------|-------| | 1 | 10 | 10 | 44 | A | | 2 | 9 | 5 | 42 | A | | 3 | 7 | 8 | 25 | A | | 4 | 3 | 22 | 65 | B | | 5 | 2 | 28 | 56 | B | | 6 | 11 | 9 | 32 | A | | 7 | 7 | 12 | 21 | A | | 8 | 4 | 21 | 61 | B | | 9 | 1 | 16 | 10 | B | | New Example | 3 | 10 | 42 | ? | #### Explanation of the Method The k-nearest neighbors (k-NN) algorithm is a non-parametric method used for classification and regression. In both cases, the input consists of the \( k \) closest training examples in the feature space. The algorithm works on the principle that similar points can be found in close proximity. Key steps to apply the k-NN algorithm: 1. **Calculate the distance** between the new data point and all existing data points. 2. **Sort** the distances to identify the nearest neighbors. 3. **Determine the majority class** among these neighbors. 4. **Classify** the new data point based on the majority class. ##### Illustration Assuming the use of Euclidean distance, you would calculate the distance from the new example to each existing data point as follows: - Distance formula for Euclidean distance: \[ \text{distance} = \sqrt{(GEN1_{new} - GEN1_{i})^2 + (GEN2_{new} - GEN2_{i})^
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