Use scikit$-$learn $,$numpy,pandas,matplotlib

Data Acquisition and Initial Analysis:

Retrieve the MNIST dataset.

Perform exploratory data analysis to understand the dataset's structure, including

i$.$ how many images

ii$.$ how many features and the range of feature values $($e$.$g$.,$ histogram of the data value$),$ relating it to real$-$world, such as real images.

iii. how many categories$/$labels $($discrete or continuous type$)$ and what they are?

iv$.$ visualize at least three randomly selected samples within each category $($feel the variance of the data$)$

v$.$ visualize more data samples to see whether there are bad data samples need to be removed. What bad data samples do you think can be$?$

Data Preparation and Manipulation:

Apply dimensionality reduction techniques $($PCA and t$-$SNE$)$ to the MNIST dataset and visualize the results.

Split the dataset into training $(60,000$ samples$)$ and testing $(10,000$ samples$)$ sets.

Machine Learning Model Implementation:

Train a Random Forest classifier on the original dataset and record its performance.

Use PCA to reduce the dataset's dimensionality to $174.$ Train a new Random Forest classifier on the reduced dataset and see how long it takes. Was training much faster? Then, evaluate the classifier on the test set. How does it compare to the previous classifier?

Critical Evaluation and Conclusion:

Provide a comprehensive evaluation of the performance of the models.

Summarize findings and insights.

Research Question: Explore how various image preprocessing methods $($e$.$g$.,$ normalization, binarization, noise reduction, and image augmentation$)$ influence the performance of at least two different machine learning models $($e$.$g$.,$ Convolutional Neural Networks and Random Forest classifiers$)$ trained on the MNIST dataset. Analyze the models' accuracy, training time, and ability to generalize to test data. Discuss your findings' implications for designing machine learning pipelines in digit recognition tasks.

Reflect on the composition and diversity of the MNIST dataset, considering its impact on the training process and model performance. Explore how the inclusion of a more diverse set of handwriting samples $($e$.$g$.,$ different handwriting styles, inclusion of characters from non$-$Latin alphabets, or samples from wider age