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Update page 'Questions concerning R language'

xuanyi.wang
2023-05-22 20:41:52 +02:00
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Questions concerning R language.md
+9 -10
@@ -13,8 +13,7 @@ This problem involves the `OJ` data set which is part of the `ISLR` package.
***Conceptual Question***
Here we explore the maximal margin classifier on a toy data set.
* We are given n = 7 observations in p = 2 dimensions. For each observation, there is an associated class label.
* i. We are given n = 7 observations in p = 2 dimensions. For each observation, there is an associated class label. Sketch the observations.
| Obs. | X1 | X2 | Y |
| -------- | -------- | -------- | -------- |
@@ -26,14 +25,14 @@ Here we explore the maximal margin classifier on a toy data set.
| 6 | 4 | 3 | Blue |
| 7 | 4 | 1 | Blue |
Sketch the observations.
* Sketch the optimal separating hyperplane, and provide the equa- tion for this hyperplane.
* Describe the classification rule for the maximal margin classifier. It should be something along the lines of “Classify to Red if β0 + β1X1 + β2X2 > 0, and classify to Blue otherwise.” Provide the values for β0, β1, and β2.
* On your sketch, indicate the margin for the maximal margin hyperplane.
* Indicate the support vectors for the maximal margin classifier.
* Argue that a slight movement of the seventh observation would not affect the maximal margin hyperplane.
* Sketch a hyperplane that is not the optimal separating hyper- plane, and provide the equation for this hyperplane.
* Draw an additional observation on the plot so that the two classes are no longer separable by a hyperplane.
* ii. Sketch the optimal separating hyperplane, and provide the equa- tion for this hyperplane.
* iii. Describe the classification rule for the maximal margin classifier. It should be something along the lines of “Classify to Red if β0 + β1X1 + β2X2 > 0, and classify to Blue otherwise.” Provide the values for β0, β1, and β2.
* iv. On your sketch, indicate the margin for the maximal margin hyperplane.
* v. Indicate the support vectors for the maximal margin classifier.
* vi. Argue that a slight movement of the seventh observation would not affect the maximal margin hyperplane.
* vii. Repeat parts (ii) through (v) using a support vector machine with a polynomial kernel. Set `degree=2`.
Sketch a hyperplane that is not the optimal separating hyper- plane, and provide the equation for this hyperplane.
* viii. Draw an additional observation on the plot so that the two classes are no longer separable by a hyperplane.