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Ostrovityanka [42]
3 years ago
14

For any two documents x and z, define k(x; z) to equal the number of unique words that occur in both x and z (i.e., the size of

the intersection of the sets of words in the two documents). Is this function a kernel? Justify your answer. Remember k(x; z) is a kernel if there exists (x) such that k(x; z) = (x)T (z)
Mathematics
1 answer:
liq [111]3 years ago
7 0

Answer:

Yes, the function is a kernel

Step-by-step explanation:

Given

Document x an z

Function definition! k(x:z)

We want to show that the above is a kernel.

To do this, we'll explicitly construct feature vectors φ(x) and φ(z)

This gives;

K(x,z) =φ(x)·φ(z).

Given than any document; say x and z

A vocabulary V can be constructed.

Vocabulary V must have a finite size of words in the document set..

The feature mapping is constructed as φ(x) for x by the following:

For the kth word wk in V, if wk appears in document x, assign φ(x) k(the kth element ofφ(x)) to be 1; else φ(x)k to 0.

Then the number of unique words common in x and z is φ(x)·φ(z), giving us the kernel

.

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In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of third angle os 88 degrees
Volgvan

Answer:

Answers: 46, 23, and 111

Step-by-step explanation:

To answer, we need to know the angles. Therefore, give each angle a name. Angle 1 will be x, 2 will be y, 3 will be z. So, using this system of equations:

x=2y

z=y+88

x+y+z=180

Substituting, z = 1/2(x)+88, now plug z into the third equation:

x+1/2(x)+1/2(x)+88=180

this simplifies to 2x+88=180

subtracting 88 from both sides leaves 2x=92

x=46

plug this in to the first equation: 46 = 2y, so y = 23

plug this into the third one leaves z = 111

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3 years ago
On a trip to Griffith Observatory, Dave rode his bicycle six more than twice as many miles in the afternoon as in the morning. I
podryga [215]

Answer:

Dave rode his bicycle 17 miles in the morning

Dave rode his bicycle 40 miles in the afternoon

Step-by-step explanation:

* Lets study the information to solve the question

- Dave rod his bicycle in the morning and again in the afternoon

- Six more than twice as many miles in the afternoon as in the morning

  means the distance in the afternoon is 6 more than twice the distance

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* To solve the question let the distance in the morning is x miles

∵ The distance in the morning = x miles

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∴ x + (2x + 6) = 57 ⇒ simplify

∴ 3x + 6 = 57 ⇒ subtract 6 from both sides

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∴ The distance in the afternoon = 2(17) + 6 = 34 + 6 = 40 miles

∴ Dave rode his bicycle 40 miles in the afternoon

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Step-by-step explanation:

8.27+6.65=14.92

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