For all the people out these getting confused, this is simple maths :( In the previous module (2.3 Perceptrons), he clearly gave the conditions. Try watching that one before coming here. They were that point (0,0) should lie on one half of the plane and the points (0,1), (1,0) and (1,1) should like on the other half of the separating plane. Consider this as something you will compare your solution to. Let us look at the first two examples he took: Example 1: For w1=-1and w2=-1, the equation of line that we get is: -1 + (-1)*x1 + (-1)*x2 = 0 => x2 = (-1)*x1 + (-1) Now, the line you get by putting (w1=-1, w2=-1) is x2 = (-1)*x1 + (-1). This is nothing but a line with slope -1 and intercept on x2 axis at -1. Let us see how it has separated the points: Point (0,0) is on the right half of the plane => Incorrect (as it should be on the left) Point (0,1) is on the right half of the plane => Correct Point (1,0) is on the right half of the plane => Correct Point (1,1) is on the right half of the plane => Correct Number of incorrect answers = 1 Example 2: For w1=1.5 and w2=0, the equation of line that we get is: -1 + 1.5*x1 + 0*x2 = 0 => x1 = 0.67 Now, the line you get by putting (w1=1.5, w2=0) is x1 = 0.67. This is nothing but a vertical line parallel to x2 axis cutting x1 at point 0.67. Let us see how it has separated the points: Point (0,0) is on the left half of the plane => Correct Point (0,1) is on the left half of the plane => Incorrect (because it should be on the right) Point (1,0) is on the right half of the plane => Correct Point (1,1) is on the right half of the plane => Correct Number of incorrect answers = 1
After looking at this problem for 3hrs ,I finally figured out how the number of errors are getting calculated.... So let first draw the straight line by the given values of w1, w2 and w3. If we taje the first example, w1 = -1, w2 = -1 and w3 = -1, so after drawing the straight line according to these values we need to check for the positions of those 4 points (0,0) (0,1) (1,0) (1,1) Here we are implementing the OR function so we need to remember for which values of x1 and x2, the outputs were showing 0 and for which values it was showing 1 As we learned in the previous lectures that if for a value of x1 and x2 ,the output is 0 then it should lie bellow the straight line that we have drawn using given w1, w2 and w3 values , and if the output is 1 then it should lie above the straight line. In this case we can see that the value x1=0 and x2 = 0 gives the output 0 so as per the perceptron rule it should lie bellow the straight line but the (0,0 ) point is lieying above the straight line and that is an error. For the remaining 3 inputs (0,1) (1,0) (1,1), the output is 1 [as we are implementing OR gate ], and these points are lied above the straight line and these are correct So for the example 1 the number of errors is 1 And for other examples also, first we need to draw the straight line , then we need to observe the position of those 4 points, then we need to calculate the outputs, for the input values that show output 1, should lie above the straight line but if any of them lies bellow the line it is an error As we can see in the example 3, the (0,1) input shows the output 1 [ OR gate] but it lies bellow or at the left side of the straight line ,but it should be on the right side, so this is an error So for the 3rd example, all the points and lieying bellow the straight line but for (0,1) (1,0) (1,1) the output is 1 [ OR gate], so it should lie above the straight line and as it is not, there are 3 errors The (0,0) shows the output 0 [ OR gate ] and it is lieying bellow the straight line and this is correct, so for example 3, one input is correct and 3 inputs are wrong, so the number of errors is 3. I hope this helps, if you have any doubt remaining, don't hesitate to reply
On the second slide it should be: For the OR function, an error occurs if (x1,x2)=(0,0) but -w0+w1*x1+w2*x2 > 0 instead of >= 0, because =0 would be correct. And if (x1,x2)!=(0,0) but -w0+w1*x1+w2*x2
please correct me as I am confused with the third line, for values of 0.45 and 0.45 that line shouldn't be where it is shown in the graph I feel, I guess the values are 45 and 45 instead of 0.45 and 0.45 ??
No, its correct. You should see where the line intersects the x1 and x2 axis while making the x2 and x1 as 0. 0.45x1 + 0.45x2 = 1, so it should be x1 = 20/9 on x1 axis and x2 = 20/9 on x2 axis.
SIMPLISTIC EXPLANATION OF THE ERROR PART ::😅 Here in this explanation i'll take only one line that is , -1+(-1)x1+(-1)x2=0; This line must have to follow the base line(i.e -1+1.1x1+1.1x2=0 as it's fixed) characteristics i.e (0,0) falls on LHS and (0,1),(1,1),(1,0) falls on RHS. But here in the example the line has only one problem that is (0,0) it's fall on RHS so it's a problem others are placed on RHS which is satisfy the condition of base line. So that's why the error is 1 for this line.
For w1=-1and w2=-1, the equation of line that we get is: -1 + (-1)*x1 + (-1)*x2 = 0 => x2 = (-1)*x1 + (-1) Now, from the previous module (2.3 Perceptrons), he clearly gave the conditions. They were that point (0,0) should lie on one half of the plane and the points (0,1), (1,0) and (1,1) should like on the other half of the separating plane. Consider this as something you will compare your solution to. Now, the line you get by putting (w1=-1, w2=-1) is x2 = (-1)*x1 + (-1). This is nothing but a line with slope -1 and intercept on x2 axis at -1. Let us see how it has separated the points: Point (0,0) is on the right half of the plane => Incorrect (as it should be on the left) Point (0,1) is on the right half of the plane => Correct Point (1,0) is on the right half of the plane => Correct Point (1,1) is on the right half of the plane => Correct So, how many errors did you get? (Compare with the original conditions I just mentioned before) We got only 1 error.
@@sidddddddddddddd Sir never mentioned that (0, 0) has to be on left side. I think the net input value has to be less than 0 for (0, 0) (see table of previous lec) which (0, 0) is satisfying and for rest it has to be greater or equal to 0 (which they are not satisfying). So, I think it should be 3 errors for w1 = w2 = -1. 😃
For all the people out these getting confused, this is simple maths :( In the previous module (2.3 Perceptrons), he clearly gave the conditions. Try watching that one before coming here. They were that point (0,0) should lie on one half of the plane and the points (0,1), (1,0) and (1,1) should like on the other half of the separating plane. Consider this as something you will compare your solution to. Let us look at the first two examples he took:
Example 1: For w1=-1and w2=-1, the equation of line that we get is:
-1 + (-1)*x1 + (-1)*x2 = 0
=> x2 = (-1)*x1 + (-1)
Now, the line you get by putting (w1=-1, w2=-1) is x2 = (-1)*x1 + (-1). This is nothing but a line with slope -1 and intercept on x2 axis at -1. Let us see how it has separated the points:
Point (0,0) is on the right half of the plane => Incorrect (as it should be on the left)
Point (0,1) is on the right half of the plane => Correct
Point (1,0) is on the right half of the plane => Correct
Point (1,1) is on the right half of the plane => Correct
Number of incorrect answers = 1
Example 2: For w1=1.5 and w2=0, the equation of line that we get is:
-1 + 1.5*x1 + 0*x2 = 0
=> x1 = 0.67
Now, the line you get by putting (w1=1.5, w2=0) is x1 = 0.67. This is nothing but a vertical line parallel to x2 axis cutting x1 at point 0.67. Let us see how it has separated the points:
Point (0,0) is on the left half of the plane => Correct
Point (0,1) is on the left half of the plane => Incorrect (because it should be on the right)
Point (1,0) is on the right half of the plane => Correct
Point (1,1) is on the right half of the plane => Correct
Number of incorrect answers = 1
thank you so much brother
Thanks a lot.
Thanks bro
Thanks a lot for your explanation. I was really stuck to this confusion. You made me out of this doubt. Thanks again 😊
Thanks a ton for this explanation
After looking at this problem for 3hrs ,I finally figured out how the number of errors are getting calculated....
So let first draw the straight line by the given values of w1, w2 and w3. If we taje the first example, w1 = -1, w2 = -1 and w3 = -1, so after drawing the straight line according to these values we need to check for the positions of those 4 points (0,0) (0,1) (1,0) (1,1)
Here we are implementing the OR function so we need to remember for which values of x1 and x2, the outputs were showing 0 and for which values it was showing 1
As we learned in the previous lectures that if for a value of x1 and x2 ,the output is 0 then it should lie bellow the straight line that we have drawn using given w1, w2 and w3 values , and if the output is 1 then it should lie above the straight line.
In this case we can see that the value x1=0 and x2 = 0 gives the output 0 so as per the perceptron rule it should lie bellow the straight line but the (0,0 ) point is lieying above the straight line and that is an error. For the remaining 3 inputs (0,1) (1,0) (1,1), the output is 1 [as we are implementing OR gate ], and these points are lied above the straight line and these are correct
So for the example 1 the number of errors is 1
And for other examples also, first we need to draw the straight line , then we need to observe the position of those 4 points, then we need to calculate the outputs, for the input values that show output 1, should lie above the straight line but if any of them lies bellow the line it is an error
As we can see in the example 3, the (0,1) input shows the output 1 [ OR gate] but it lies bellow or at the left side of the straight line ,but it should be on the right side, so this is an error
So for the 3rd example, all the points and lieying bellow the straight line but for (0,1) (1,0) (1,1) the output is 1 [ OR gate], so it should lie above the straight line and as it is not, there are 3 errors
The (0,0) shows the output 0 [ OR gate ] and it is lieying bellow the straight line and this is correct, so for example 3, one input is correct and 3 inputs are wrong, so the number of errors is 3.
I hope this helps, if you have any doubt remaining, don't hesitate to reply
i watch these perceptron video whole day and then next day i am able to understand ... explaination is hard it is for brilliant student ...
This tutor is good with his own knowledge but he need training on tutoring,
I didn't get how error value is getting ....plz explain any one
Should have included the raw equation in second slide! It was so confusing
i didn't get how error value get calculated.....Any one can explain?
On the second slide it should be:
For the OR function, an error occurs if (x1,x2)=(0,0) but -w0+w1*x1+w2*x2 > 0 instead of >= 0, because =0 would be correct.
And if (x1,x2)!=(0,0) but -w0+w1*x1+w2*x2
please correct me as I am confused with the third line, for values of 0.45 and 0.45 that line shouldn't be where it is shown in the graph I feel, I guess the values are 45 and 45 instead of 0.45 and 0.45 ??
No, its correct. You should see where the line intersects the x1 and x2 axis while making the x2 and x1 as 0.
0.45x1 + 0.45x2 = 1, so it should be x1 = 20/9 on x1 axis and x2 = 20/9 on x2 axis.
merci
make a play list for better acess
I am not understanding here what is the meaning of error and how many error could anybody please help me to explai?
w1=-1 w2=-1 under that cond there ll be 3 errors
💀💀💀
❤❤❤❤❤❤❤❤
Great, Great
did u know any other source that explain same this material or material like this.... please tell me it will be thankful
SIMPLISTIC EXPLANATION OF THE ERROR PART ::😅
Here in this explanation i'll take only one line that is ,
-1+(-1)x1+(-1)x2=0;
This line must have to follow the base line(i.e -1+1.1x1+1.1x2=0 as it's fixed) characteristics i.e (0,0) falls on LHS and (0,1),(1,1),(1,0) falls on RHS.
But here in the example the line has only one problem that is (0,0) it's fall on RHS so it's a problem others are placed on RHS which is satisfy the condition of base line.
So that's why the error is 1 for this line.
Hey, how is errors as 3 for w1 = 0.45 and w2 = 0.45 ? can you explain please ?
i think for condition (w1,w2) = (-1,-1) the errors are 3 ... Correct me if i am wrong
Check my response above.
For w1=-1and w2=-1, the equation of line that we get is:
-1 + (-1)*x1 + (-1)*x2 = 0
=> x2 = (-1)*x1 + (-1)
Now, from the previous module (2.3 Perceptrons), he clearly gave the conditions. They were that point (0,0) should lie on one half of the plane and the points (0,1), (1,0) and (1,1) should like on the other half of the separating plane. Consider this as something you will compare your solution to.
Now, the line you get by putting (w1=-1, w2=-1) is x2 = (-1)*x1 + (-1). This is nothing but a line with slope -1 and intercept on x2 axis at -1. Let us see how it has separated the points:
Point (0,0) is on the right half of the plane => Incorrect (as it should be on the left)
Point (0,1) is on the right half of the plane => Correct
Point (1,0) is on the right half of the plane => Correct
Point (1,1) is on the right half of the plane => Correct
So, how many errors did you get? (Compare with the original conditions I just mentioned before) We got only 1 error.
@@sidddddddddddddd Sir never mentioned that (0, 0) has to be on left side.
I think the net input value has to be less than 0 for (0, 0) (see table of previous lec) which (0, 0) is satisfying and for rest it has to be greater or equal to 0 (which they are not satisfying).
So, I think it should be 3 errors for w1 = w2 = -1.
😃
It's a linear inequality in two variables. For all coeffs being -1. The region on the Right side of the line satisfies x1+x2+w0
i did't get how error value is getting??
Any one can explain to me?
He continued with the previous example boolean OR all 0 on one side of the line and all ones on another side of the line.