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Consider an attribute X of a data set that takes the values { x 1 , x 2 , , x 9 } ( sorted

Consider an attribute X of a data set that takes the values {x1, x2,, x9}
(sorted in increasing order of magnitude). We apply two methods (equal
interval width and equal frequency) to discretize the attribute into three
bins. The bins obtained are shown below:
Equal Width: {x1, x2, x3},{x4, x5, x6, x7, x8},{x9}
Equal Frequency {x1, x2, x3},{x4, x5, x6},{x7, x8, x9}
Explain what will be the effect of applying the following transformations on
each discretization method, i.e., whether the elements assigned to each bin
can change if you discretize the attribute after applying the transformation
function below. Note that X denotes the average value and \sigma x denotes
standard deviation of attribute X.
The answer to each subquestion is a dictionary with two keys: equal width
and equal freq. The values of each key is a list of two values: a string and
an integer. The string is either Change or No change. The value of the
integer is chosen among (1,...,10), chosen according to the list below:
1. The transformation leads to an inversion of the original order of values.
2. The distance between xi and xi+1 does not change uniformly.
3. The average value X becomes the smallest value post-transformation.
4. The relative ordering of points changes
5. The transformation causes negative values to become positive and vice
versa.
6. The transformation results in all values becoming equal.
3
7. The distance between xi and xi+1 change uniformly.
8. The standard deviation \sigma X becomes zero after the transformation.
9. No change in the relative ordering of points
10. The maximum and minimum values of X get swapped after the transformation.
Subquestions to answer:
(a) X -> X x,(i.e., if the attribute values are centered).
(b) X -> XX
\sigma x
,(i.e., if the attribute values are standardized).
(c) X -> exp h
XX
\sigma x
i
(i.e., if the values are standardized and exponentiated).Consider an attribute X of a data set that takes the values {x1, x2,, x9}
(sorted in increasing order of magnitude). We apply two methods (equal
interval width and equal frequency) to discretize the attribute into three
bins. The bins obtained are shown below:
Equal Width: {x1, x2, x3},{x4, x5, x6, x7, x8},{x9}
Equal Frequency {x1, x2, x3},{x4, x5, x6},{x7, x8, x9}
Explain what will be the effect of applying the following transformations on
each discretization method, i.e., whether the elements assigned to each bin
can change if you discretize the attribute after applying the transformation
function below. Note that X denotes the average value and \sigma x denotes
standard deviation of attribute X.
The answer to each subquestion is a dictionary with two keys: equal width
and equal freq. The values of each key is a list of two values: a string and
an integer. The string is either Change or No change. The value of the
integer is chosen among (1,...,10), chosen according to the list below:
1. The transformation leads to an inversion of the original order of values.
2. The distance between xi and xi+1 does not change uniformly.
3. The average value X becomes the smallest value post-transformation.
4. The relative ordering of points changes
5. The transformation causes negative values to become positive and vice
versa.
6. The transformation results in all values becoming equal.
3
7. The distance between xi and xi+1 change uniformly.
8. The standard deviation \sigma X becomes zero after the transformation.
9. No change in the relative ordering of points
10. The maximum and minimum values of X get swapped after the transformation.
Subquestions to answer:
(a) X -> X x,(i.e., if the attribute values are centered).
(b) X -> XX
\sigma x
,(i.e., if the attribute values are standardized).
(c) X -> exp h
XX
\sigma x
i
(i.e., if the values are standardized and exponentiated).

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