CS 345 FINAL EXAMINATION TEST
COMPLETE QUESTIONS AND ANSWERS
FULL SOLUTION VERIFIED
●● What does it mean to add more dimension to a problem/dataset
Answer: add more features/variables
●● What is the norm of a vector
Answer: the length. Norm of vector in 2 dimensions means find the
hypotenuse (Pythagorean theorem)
●● What is a unit vector?
Answer: a vector with a norm = 1. To make a vector a unit vector, divide
by its norm. This vector points in the direction of the original vector.
●● What makes up any vector
Answer: length and direction (norm and unit vector).
u^=u/||u||
●● What is normalization
Answer: dividing a vector by its norm to get the unit vector.
,●● What does the dot product of two vectors measure?
Answer: measures how closely two vectors align in terms of directions
they point. Closely related to the angle between the two vectors. Equal
to the cosine of the angle between them. multiple two vectors together
essentially feature by feature.
●● What is it called when the dot product is equal to 0.
Answer: orthogonal vectors
●● What is the angle between orthogonal vectors?
Answer: orthogonal vectors are perpendicular to each other, so 90
degree angle. cos(90) = 0.
●● What can you say about the angle between vectors that have positive
coefficients?
Answer: positive coefficients imply that all the components of the
vectors are positive. If vectors are in the same direction, angle is 0. If
opposite directions, angle is 180.
●● What is the norm of a vector as a dot product?
Answer: the norm (or magnitude) of a vector as a dot product is
expressed as a dot product of the vector with itself.
, ●● What is the square root of the dot product?
Answer: the euclidean norm
●● What does it mean for dot products to be negative or positive?
Answer: Negative is not similar directions, so not similar features.
Positive is similar directions and features.
●● Describe what a hyperplane is
Answer: a key mathematical object that gives rise to linear classifiers as
the simplest examples. It is the decision boundary. if the bias (b) = 0
then the hyperplane goes through the origin. the dot product of the input
vector, the weight vector, and the bias term gives a score. the sign of that
score determines what side of the hyperplane that feature is on. Different
class on each side.
●● What is parameter w
Answer: w is the weight vector and it assigns a weight to each feature.
●● what is parameter b
Answer: additional parameters for flexibility and determines the position
of the hyperplane. it is the bias term.
●● Describe the perceptron and inputs and outputs
COMPLETE QUESTIONS AND ANSWERS
FULL SOLUTION VERIFIED
●● What does it mean to add more dimension to a problem/dataset
Answer: add more features/variables
●● What is the norm of a vector
Answer: the length. Norm of vector in 2 dimensions means find the
hypotenuse (Pythagorean theorem)
●● What is a unit vector?
Answer: a vector with a norm = 1. To make a vector a unit vector, divide
by its norm. This vector points in the direction of the original vector.
●● What makes up any vector
Answer: length and direction (norm and unit vector).
u^=u/||u||
●● What is normalization
Answer: dividing a vector by its norm to get the unit vector.
,●● What does the dot product of two vectors measure?
Answer: measures how closely two vectors align in terms of directions
they point. Closely related to the angle between the two vectors. Equal
to the cosine of the angle between them. multiple two vectors together
essentially feature by feature.
●● What is it called when the dot product is equal to 0.
Answer: orthogonal vectors
●● What is the angle between orthogonal vectors?
Answer: orthogonal vectors are perpendicular to each other, so 90
degree angle. cos(90) = 0.
●● What can you say about the angle between vectors that have positive
coefficients?
Answer: positive coefficients imply that all the components of the
vectors are positive. If vectors are in the same direction, angle is 0. If
opposite directions, angle is 180.
●● What is the norm of a vector as a dot product?
Answer: the norm (or magnitude) of a vector as a dot product is
expressed as a dot product of the vector with itself.
, ●● What is the square root of the dot product?
Answer: the euclidean norm
●● What does it mean for dot products to be negative or positive?
Answer: Negative is not similar directions, so not similar features.
Positive is similar directions and features.
●● Describe what a hyperplane is
Answer: a key mathematical object that gives rise to linear classifiers as
the simplest examples. It is the decision boundary. if the bias (b) = 0
then the hyperplane goes through the origin. the dot product of the input
vector, the weight vector, and the bias term gives a score. the sign of that
score determines what side of the hyperplane that feature is on. Different
class on each side.
●● What is parameter w
Answer: w is the weight vector and it assigns a weight to each feature.
●● what is parameter b
Answer: additional parameters for flexibility and determines the position
of the hyperplane. it is the bias term.
●● Describe the perceptron and inputs and outputs
