Question

Suppose a 2-dimensional data set D is linearly separable, and the line that separates them has equation: 2+ 3x1 - 4x2 Now, let's assume that we want to do a standardization of the data set D. And that results in the following transformation: if a point has attributes (a,b) then the standardized data point will have attributes (a/3, 2xb). Fill the blanks in the following equation, so that it separates the transformed data set. [Hint: check the equation for the original set and try to transform it accordingly]

Answer 1

After standardizing the original 2-dimensional dataset by using the transformation (a/3, 2xb), the new linear separation equation transforms to 2 + x1 - 8x2.

Step-by-step explanation:

To find the equation that separates the transformed dataset after standardization, we utilize the given equation for the original set, which is 2 + 3x1 - 4x2 = 0.

To transition this to the transformed scale, we have to incorporate the scaling factors for each variable. Given the transformation, a standardized point (a/3, 2xb) corresponds to the original point (a, b).

Therefore, we substitute x1 with a/3 and x2 with 2xb into the original equation.

Doing the substitution, we get:

2 + 3(a/3) - 4(2xb) = 0

Simplify the equation:

2 + a - 8xb = 0

Thus, to separate the transformed dataset, our new line equation will be:

2 + x1 - 8x2