به انگلیسی

Fewer numbers, most of the spread

رایانش · یادگیری ماشین · سن ۲۰ تا ۲۲ سال

نام ______________________ تاریخ ____________

You project a two-feature dataset onto its first component. What is kept for each point?
- Both original values unchanged
- Its position along the direction of biggest spread
- Its distance from the origin only
If every feature has variance exactly 1, PCA on the covariance matrix and on the correlation matrix give the same components.
دور یکی دایره کشیدن: درست نادرست
A scree plot shows 62, 25, 8, 3 and 2 percent. How many components should you keep, and why?
- All five, since more numbers always help
- One, since only the first ever matters
- Two, since they hold most variation
For which pair of variables would it make sense to compute a correlation coefficient?
- Height and weight
- Shoe size and favorite color
- Province of residence and income bracket
- Hair color and eye color
You reduce ten correlated features to two components. What does each example become?
- Two numbers from the two components
- Ten numbers with the variation spread thin
- Two labels naming the original features
Two features have covariance 4, and their standard deviations are 2 and 4. What is their correlation? Round to two decimal places if needed.
پاسخ: ______________
You standardise every feature of a dataset so each one has mean 0 and standard deviation 1, then run PCA. A friend runs PCA on the raw covariance matrix of the same data without standardising. Which statement is true?
- Both runs always give the exact same components
- They can differ: scale tilts raw covariance
- PCA on the correlation matrix ignores how the features vary together
- Standardising the data deletes the correlations between features
Two features have covariance 4, with standard deviations 2 and 4. What is their correlation?
پاسخ: ______________
A component is 0.7 times height plus 0.7 times weight minus 0.1 times age. Why is it hard to name?
- The rows were shuffled at random
- It blends several features instead of matching one
- Height and weight can never mix
A friend keeps all five components since more numbers always help. Components hold 62, 25, 8, 3 and 2 percent. Best reply?
- Agree, extra tiny components always pay off
- Keep one, since only the first ever matters
- Keep two: they hold 87 percent

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Fewer numbers, most of the spread W1-mt_l-9XHg_ChZ-s1

Its position along the direction of biggest spread · Projection keeps one number per point: where it lands along that direction.
درست · Correlation divides by deviations of 1, which changes nothing, so both matrices match.
Two, since they hold most variation · The first two sum to 87 percent, while 8, 3 and 2 add little.
Height and weight · Correlation measures how strongly two numeric variables move together along a straight line. It only makes sense when both variables are numbers.
Two numbers from the two components · Two kept directions give two numbers per example. They hold most of the spread only when their explained shares are large; correlation alone does not set the shares.
0.5 · The correlation is the covariance divided by the product of the standard deviations: 4 divided by 2 times 4, which is 0.5.
They can differ: scale tilts raw covariance · PCA chases directions of biggest spread. On raw covariance, a feature with a large scale swamps the others, so the components can tilt toward it. Standardising gives every feature an equal say, which can change the answer.
0.5 · Divide covariance by both deviations: 4 divided by 8 is 0.5.
It blends several features instead of matching one · Blends of several original features resist clean labels in their language.
Keep two: they hold 87 percent · Stopping where gains turn tiny keeps most variation with far fewer numbers.