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