CSCI$-4343$ Data Mining

Homework $3$

Q$1(5$ pt$)$: Given a dat point of class A with attributes equal to $(x^{\text{'}}=2,y^{\text{'}}=0).$

Suppose the classifier is defined as:

if $x+y+w<mn>0</mn>$ then class A

otherwise class B

Given the loss defined as $L(w)=(x_0+y_0+w{)}^2$ if model classify it to class

B and $L(w)=0$ if the model correctly classify the point.

Suppose we randomly initialize $w=2,$ we first estimate the steep at $w=2$

use $$ we learn in the class.

$($a$)$: Please write down the slope of line that across points $(w-,L(w-))$ and

$(w+,L(w+))$ when $=10?$

$($b$)$: What if $=5,=1$ or $=0\mathrm{.}1?$

$($c$)$: Please use gradient to compute the steep at $w=2($Hint: substitute $x^{\text{'}}$ and

$y^{\text{'}}$ with the values and then compute gradient$).$ Feel free to use calculator such

as Wolfram to perform computation.

$($d$)$ Write down first two steps of gradient descend algorithm over $L(w)$ start$-$

ing with $w=2$ and learning rate $=0\mathrm{.}1.$