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# QMNIST Feature Reduction

In this project we apply PCA to QMNIST data. Read about Feature Reduction before you start.

## Preprocessing

Task: Use the Python module developed in Load QMNIST to load the first 5000 QMNIST training images.

Solution:

    # your solution

Task: Use the above module to apply the following preprocessing steps from Image Processing with NumPy

- auto crop,

- center in 20x20 image

Solution:

    # your solution

## Relevant Components

Task: Perform a full PCA (no feature reduction) and plot standard deviations (square roots of variances) for all principal components.

Solution:

    # your solution

Task: Show the data set’s mean and the first 100 principal components as images. Scale principal components by corresponding standard deviation and use same color map for all images.

Solution:

    # your solution

Task: Transform all images by PCA with 15 components. For one images plot original and transformed image side by side (you may use `PCA.inverse_transform` or implement calculations manually).

Solution:

    # your solution

## Visualization

We may use feature reduction techniques to visualize high-dimensional data sets.

Task: Use PCA to reduce the data set to 3 features. Plot the now 3d data set. Color classes differently.

    # your solution

Task: Use PCA to reduce the data set to 4 features. Make pair plots for combinations of two features (use same coloring as above).

    # your solution