Suppose that you have the following collection T of data points in two dimensions: x|1 |1 |2 | 3 | 4 y 13 2 4 2 B BRRB The picture below illustrates these points, together with the classifier if a + y - 3 > 0 then BLUE else RED, corresponding to the weight vector (1, 1, 3). DO 3 E 1 Classified blue Classified red 2 3 4 A. Compute the value of the error function for this classifier: Σ PET,p misclassified Er () = JWiPz + wzPy - wa| 2.
Suppose that you have the following collection T of data points in two dimensions: x|1 |1 |2 | 3 | 4 y 13 2 4 2 B BRRB The picture below illustrates these points, together with the classifier if a + y - 3 > 0 then BLUE else RED, corresponding to the weight vector (1, 1, 3). DO 3 E 1 Classified blue Classified red 2 3 4 A. Compute the value of the error function for this classifier: Σ PET,p misclassified Er () = JWiPz + wzPy - wa| 2.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Transcribed Image Text:Suppose that you have the following collection T of data points in two dimensions:
1
4.
1
4 2
B.
3
2
B
R
R
The picture below illustrates these points, together with the classifier
if x +y - 3> 0 then BLUE else RED,
corresponding to the weight vector (1,1, 3).
DO
3
2
1
Classified blue
Classified red
1
3
4
A. Compute the value of the error function for this classifier:
Er (i) =
Σ
JwiPz + wzPy - ws|
PET,p misclassified
B. Compute the gradient of the error function with respect to the weight vector w. The gradient is
a vector VE = (91,92, 93) computed as follows: For a given weight vector i and data point p €T
let
if pis labelled RED in T but is classified BLUE by i
-1 if p is labelled BLUE in T but is classified RED by w
if p is correctly classified by u
( 1
sz(p) =
Then
VE =E sa(p) · (Pz. Py, -1)
PET
C. Compute the new weight vector after one step of gradient descent: u = w - 6 . VE where
8 = 0.1.
D. How does the new weight vector u' classify the points?
E. What is the value of the error function at the new weight vector ?
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