$${\color{blue}Crypto \ Clustering}$$

Cluster Cryptocurrencies with K-Means, Finding Elbow Curve, and Optimize Clusters with Principal Component Analysis.

In Step 1, we imported the necessary libraries and loaded data with "coin_id" as the index column.

The sci-kit-learn (sklearn) library was used to conduct the KMeans clusters, Principle Component Analysis, and StandardScaler to fit and transform the data.

# Import required libraries and dependencies

import pandas as pd
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
import matplotlib.pyplot as plt

Step 2 is to Prepare the Data by conducting preprocessing.

We need to use StandardScaler() module from sci-kit-learn to normalize the data from the 'market_data_df' DataFrame.
This step includes using StandardScaler() and then fit transforming the data.
StandardScaler() = is used to standardize the features in the DataFrame by removing the mean and scaling to unit variance (z-score normalization).
The fit_transform() method computes the necessary statistics (mean and standard deviation) on market_data_df and
Then apply the transformation to the data. The result is a NumPy array where each feature has been scaled.

DataFrame after preprocessing:

The next step during the preprocessing is to verify the data:

Verify that the mean of each feature (column) is 0: (ADD IMAGES)

Verify that the std of each feature (column) is 1: (ADD IMAGES)

In Step 3, we will create a DataFrame with the scaled data, setting the Coin_id Column as the Index.

DateFrame of scaled data:

$${\color{blue}K-Means \space Clustering}$$

Step 4 is to initialize the list to store 'k' and loop to Fit K-Means and Compute Inertia:

This step aims to initiate the empty list inertia = [] to store the different values of 'k'.
Inertia will store the sum of the squared distances of samples at their closest cluster center. This is used to evaluate clustering quality).
k is a range of cluster counts to test (from 1 to 10).

# Create a list to store inertia values
inertia = []

# Create a list to store the values of k
k = list(range(1, 11))

for i in k:
    k_model = KMeans(n_clusters=i, random_state=2)
    k_model.fit(scaled_marketdata_df)
    inertia.append(k_model.inertia_)

In Step 5 we need to Find the Best Value for k Using the Original Scaled DataFrame.

During this step, we take the "inertia" list we lopped through in the previous step and create a DataFrame called elbow_data.
During this step, you also want to visualize the elbow curve.

K-Means Elbow Curve

This plots the number of clusters (k) on the x-axis against the inertia on the y-axis.
The "Elbow Curve" helps to identify the optimal number of clusters by looking for the "elbow" point where inertia starts to decrease more slowly.
This point often suggests a good balance between model complexity and fit quality. Question: What is the best value for k? 4

$${\color{blue}K-Means \space Clustering \space on \space Scaled \space Data}$$

Step 6 Applies K-means clustering to the scaled data to group cryptocurrencies into clusters.

During this step, we use the optimal number from the previous analysis (Step 5) and initialize the K-Means model with 4 clusters and a fixed random seed for reproducibility.

model = KMeans(n_clusters=4, random_state=1)
model.fit(scaled_marketdata_df)

We then fit the K-Means model to the scaled market data.
Lastly, we assign cluster labels to each data point based on the fitted model.

k_lower = model.predict(scaled_marketdata_df)'

k_lower now includes the cluster predictions which we will use in the next step.

Adding Cluster Predictions to DF and Visualizing the Clusters on a scatter plot.

Step 7 includes adding the cluster predictions into a DataFrame to create a scatter plot to visualize it.

Here we will be creating a copy of the scaled_marketdata_df and adding a new column with the k_lower from Step 6

scaled_marketdata_prediction['Predicted Clusters'] = k_lower'

Scatter Plot for K-Means Clusters

In this scatter plot we set x="price_change_percentage_24h" and y="price_change_percentage_7d".

$${\color{blue}Principal \space Component \space Analysis \space (PCA)}$$

Step 8 is to create a DataFrame with PCA Components similar to other previous analyses.

During this step, we will create a PCA model and set the number of principal components to 3.
- The fit transform performs PCA on the scaled data, transforming it into a three-dimensional space.

PCA = PCA(n_components=3)
PCA_market_scaled = PCA.fit_transform(scaled_marketdata_df)

Step 9 includes Plotting Elbow Curve

The elbow curve is the same as the K-Means analysis.

PCA Elbow Curve

Step 10 includes conducting similar steps as the K-Means and Creating a scatter plot

Initializing the K-Means models, fitting, predicting clusters, and adding the predicted clusters to a DF with a new column.

# Initialize the K-Means model using the best value for k
k = KMeans(n_clusters=4, random_state=1)

# Fit the K-Means model using the PCA data
k.fit(pca_df_marketdata)

# Predict the clusters to group the cryptocurrencies using the PCA data
k_model = k.predict(pca_df_marketdata)

# Create a copy of the DataFrame with the PCA data
k_model_copy = pca_df_marketdata.copy()
#---

# Add a new column to the DataFrame with the predicted clusters
k_model_copy['Predict Cluster'] = k_model

#---

# Create a scatter plot using hvPlot by setting `x="PCA1"` and `y="PCA2"`. 
k_model_copy.plot.scatter(
    x="PCA1",
    y="PCA2",
    c=k_model,
    colormap='rainbow')

Scatter plot visualizing PCA Clusters

In Step 11, we transpose the features to retrieve the weights of the principal components.

During this step, we will create a DataFrame called components_weights_pca that transposes the features.
Each column represents the weight of that feature in each principal component. (ADD IMAGE OF TRANSPOSE)

components_weights_pca = pd.DataFrame(PCA.components_.T,columns=['PCA1', 'PCA2', 'PCA3'], 
                                      index=scaled_marketdata_df.columns)'
components_weights_pca

$${\color{blue}Interpretation \space of \space the \space Results.}$$

For PCA1, price_change_percentage_200d (0.594468) and price_change_percentage_1y (0.568379) have the strongest positive influence, while price_change_percentage_24h (-0.416728) has the strongest negative influence.
For PCA2, price_change_percentage_30d (0.562182) and price_change_percentage_14d (0.540415)have the strongest positive influence, while price_change_percentage_1y (-0.150789) has the strongest negative influence.
For PCA3, price_change_percentage_7d (0.787670) and price_change_percentage_14d (0.349534) have the strongest positive influence, while price_change_percentage_60d (-0.361377) has the strongest negative influence.

ElphysAlvarez01/CryptoClustering