Q$3$ PCA reconstruction

$1$ Point

Grading comment:

Select one option.

Here are some pictures of the digit $3$ in the MNIST dataset, dataset of $60,000$ small square $28\backslash$times $28$ pixel grayscale images of handwritten single digits between $0$ and $9.$ We will represent each image as a vector of $784$ dimensions.

Screen$\_$Shot$\_2022-05-14\_$at$\_2\mathrm{.}14\mathrm{.}53\_$AM$.$png

Let

$$

k be the number of dimensions we are going to use for PCA.

Here are two reconstructed images:

mnist$\_3.$png

mnist$\_3\_2.$png

Which of the following assessment is not correct when we apply PCA to construct images from this dataset:

The following multiple$-$choice options contain math elements, so you may need to read them in your screen reader's $$reading$$ or $$browse$$ mode instead of $$forms$$ or $$focus$$ mode.

Choice $1$ of $4$:Using

$$

$=$

$784$

k$=784$ will yield a reconstruction error of

$0$

$0.$

Choice $2$ of $4$:Increasing

$$

k makes a reconstructed image less blurry and more similar to the original one.

Choice $3$ of $4$:Image $1$ uses less principal components to construct than Image $2.$

Choice $4$ of $4$:Image $1$ has a smaller reconstruction error than Image $2.$

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Question $3$: PCA reconstruction$*$Unsaved Changes