use only scikit learn $,$pandas,numpy and matplotlib no other libraries

please no plagiarism

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 groups$)$ might affect the accuracy and generalizability of machine learning models trained for digit

recognition tasks. Instructions

MNIST number dataset a set of $70,000$ small images of digits handwritten by high school students and

employees of the US Cen$-$ sus Bureau. Each image is labeled with the digit it represents. This set has been

studied so much that it is often called the "hello world" of Machine Learning: whenever people come up with

a new classification algorithm they are curious to see how it will perform on MNIST, and anyone who learns

Machine Learning tackles this dataset sooner or later.

Instructions to explore this dataset are:

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.