Data Fundamentals (H) - Week 04 Quiz
1. \(\|\vec{x}\|_\infty\) could be computed by which operation?
np.cumsum(x*x[::-1])
np.max(np.abs(x))
np.sqrt(np.sum(x**2))
np.sum(np.abs(x))
np.min(np.abs(x))
2. Which of these operations is
not
defined over vectors in a topological vector space equipped with an inner product?
square root
length measurement
addition
scalar multiplication
inner product
3. \(\vec{x}\bullet \vec{y}\) is zero if and only if:
\(x\) is not equal to \(y\)
\(x\) is a scaled version of \(y\)
\(x\) is orthogonal to \(y\)
\(x\) is equal to \(y\)
\(x\) is nonzero
4. Distances in high-dimension can be counter intuitive because:
There are so many different kinds of distances
Distances cannot be computed
Distances will span a huge range of possible values
Only the \(L_\infty\) norm can be applied.
Every vector will have a very similar distance to every other vector
5. The covariance matrix represents:
the colour of the dataset
the spread of the dataset around its mean
the number of non-zero elements in a dataset
the cross product of the mean vector with itself
the size of the largest element of a dataset
6. When rendering a graph with unsigned scalar values mapped to colours, what property should the colour map have?
Monotonic, perceptually nonuniform hue-saturation separation
Monotonic red-blue separation.
A diverging hue around zero.
Perceptually uniform, monotonically increasing brightness
Perceptually cuniform, moronically unceasing colour
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