1. Project Overview

A digital currency known as cryptocurrency is established on cryptographic evidence that is essential to confirm each transaction. Cryptocurrencies are distinguished by several features, including their lack of dependence on central authorities such as central banks, their provision of a degree of pseudo-anonymity, and their ability to protect against double spending attacks. in this project applies financial Python programming and unsupervised learning algorithms to categorize cryptocurrencies according to their performance during different timeframes, using K-Means and Principal Component Analysis (PCA). The dataset used in this analysis comprises a CSV file that includes returns (price fluctuations) data of cryptocurrencies across diverse time periods.
1.1. K-Means
K-means is an unsupervised machine learning algorithm used for clustering data. It aims to partition n observations into k clusters, where each observation belongs to the cluster with the nearest mean. The algorithm works by iteratively updating the cluster centroids and assigning data points to their closest centroid until convergence. K-means is widely used in various fields, including image segmentation, customer segmentation, and anomaly detection.
2.1. Principal Component Analysis (PCA)
Principal Component Analysis (PCA) is a popular technique for dimensionality reduction in machine learning. It aims to transform high-dimensional data into a lower-dimensional space while retaining as much of the original data's variation as possible. PCA works by identifying the principal components, which are the linear combinations of the original variables that explain the most variance in the data. The resulting principal components can be used as new features in machine learning models.
In [1]:
# dependencies and setup
from package.constants import * # constants
from package.helpers import * # libraries, dependencies and functions

☑ constants is imporetd
☑ helpers is imporetd

2. Data Preparation

In [2]:
# load the data into a Pandas DataFrame
df_market_data = pd.read_csv(DATA_URL+"crypto_market_data.csv", index_col="coin_id")

# display sample data
df_market_data.head()
Out[2]:
price_change_percentage_24h price_change_percentage_7d price_change_percentage_14d price_change_percentage_30d price_change_percentage_60d price_change_percentage_200d price_change_percentage_1y
coin_id
bitcoin 1.08388 7.60278 6.57509 7.67258 -3.25185 83.51840 37.51761
ethereum 0.22392 10.38134 4.80849 0.13169 -12.88890 186.77418 101.96023
tether -0.21173 0.04935 0.00640 -0.04237 0.28037 -0.00542 0.01954
ripple -0.37819 -0.60926 2.24984 0.23455 -17.55245 39.53888 -16.60193
bitcoin-cash 2.90585 17.09717 14.75334 15.74903 -13.71793 21.66042 14.49384
In [3]:
# generate the df info
df_market_data.info()

<class 'pandas.core.frame.DataFrame'>
Index: 41 entries, bitcoin to digibyte
Data columns (total 7 columns):
 #   Column                        Non-Null Count  Dtype  
---  ------                        --------------  -----  
 0   price_change_percentage_24h   41 non-null     float64
 1   price_change_percentage_7d    41 non-null     float64
 2   price_change_percentage_14d   41 non-null     float64
 3   price_change_percentage_30d   41 non-null     float64
 4   price_change_percentage_60d   41 non-null     float64
 5   price_change_percentage_200d  41 non-null     float64
 6   price_change_percentage_1y    41 non-null     float64
dtypes: float64(7)
memory usage: 2.6+ KB
In [4]:
# generate the summary statistics
df_market_data.describe(include = 'all').round(2)
Out[4]:
price_change_percentage_24h price_change_percentage_7d price_change_percentage_14d price_change_percentage_30d price_change_percentage_60d price_change_percentage_200d price_change_percentage_1y
count 41.00 41.00 41.00 41.00 41.00 41.00 41.00
mean -0.27 4.50 0.19 1.55 -0.09 236.54 347.67
std 2.69 6.38 8.38 26.34 47.37 435.23 1247.84
min -13.53 -6.09 -18.16 -34.71 -44.82 -0.39 -17.57
25% -0.61 0.05 -5.03 -10.44 -25.91 21.66 0.41
50% -0.06 3.30 0.11 -0.04 -7.54 83.91 69.69
75% 0.61 7.60 5.51 4.58 0.66 216.18 168.37
max 4.84 20.69 24.24 140.80 223.06 2227.93 7852.09
In [5]:
# plotting data
line(df_market_data,"Price Change Over Time")
In [6]:
# use the StandardScaler() module to normalize the data from the CSV file
data_scaled = StandardScaler().fit_transform(df_market_data)

# create a df for the scaled data and set the coinid column as index
df_market_scaled = pd.DataFrame(data_scaled, columns=df_market_data.columns, index=df_market_data.index)

# display sample data
df_market_scaled.head()
Out[6]:
price_change_percentage_24h price_change_percentage_7d price_change_percentage_14d price_change_percentage_30d price_change_percentage_60d price_change_percentage_200d price_change_percentage_1y
coin_id
bitcoin 0.508529 0.493193 0.772200 0.235460 -0.067495 -0.355953 -0.251637
ethereum 0.185446 0.934445 0.558692 -0.054341 -0.273483 -0.115759 -0.199352
tether 0.021774 -0.706337 -0.021680 -0.061030 0.008005 -0.550247 -0.282061
ripple -0.040764 -0.810928 0.249458 -0.050388 -0.373164 -0.458259 -0.295546
bitcoin-cash 1.193036 2.000959 1.760610 0.545842 -0.291203 -0.499848 -0.270317
In [7]:
# generate the summary statistics for scaled data
df_market_scaled.describe(include = 'all').round(2)
Out[7]:
price_change_percentage_24h price_change_percentage_7d price_change_percentage_14d price_change_percentage_30d price_change_percentage_60d price_change_percentage_200d price_change_percentage_1y
count 41.00 41.00 41.00 41.00 41.00 41.00 41.00
mean 0.00 0.00 0.00 0.00 0.00 -0.00 0.00
std 1.01 1.01 1.01 1.01 1.01 1.01 1.01
min -4.98 -1.68 -2.22 -1.39 -0.96 -0.55 -0.30
25% -0.13 -0.71 -0.63 -0.46 -0.55 -0.50 -0.28
50% 0.08 -0.19 -0.01 -0.06 -0.16 -0.36 -0.23
75% 0.33 0.49 0.64 0.12 0.02 -0.05 -0.15
max 1.92 2.57 2.91 5.35 4.77 4.63 6.09
In [8]:
# plotting scaled data
line(df_market_scaled,"Standardized Price Change Over Time")

3. Analysis and Result

Determining the best number of clusters (k) depends on the specific problem and data being analyzed. However, we can use the information provided by the three methods to make a recommendation. (1) Elbow method suggests that the optimal number of clusters is where the change in Within-Cluster Sum of Squares (WCSS) begins to level off. (2) Silhouette method measures how well each data point fits into its assigned cluster and ranges from -1 to 1, where values closer to 1 indicate a better fit. (3) Calinski-Harabasz index measures the ratio of between-cluster variance to within-cluster variance, and a higher value indicates better clustering.

1.3. Find the Best Value for k Using the Original Data.
In [9]:
# determine the optimal value of k by "clusters_methods" function in the "helpers" package located at "./src/package/helpers" is 
cluster_results, optimal_ks = clusters_methods(df_market_scaled, ["wcss_elbow", "silhouette", "calinski_harabasz"])

# plotting methods by "score_plot" function in the "helpers" package located at "./src/package/helpers"
score_plot(cluster_results, optimal_ks)
Observation

After analyzing the data and evaluating the elbow method plot, it appears that k=4 could be the optimal number of clusters as the WCSS change starts to level off around this point. However, when looking at the silhouette score, k=3 seems to be the best choice. Additionally, the Calinski-Harabasz index is highest for k=4, further indicating that this value could be optimal. Considering k=3, k=4, and possibly k=5 as reasonable options, selecting the ideal number of clusters is subjective and requires the domain knowledge and discretion.

2.3. Cluster Cryptocurrencies with K-means Using the Original Data.

Clustering the optimal value of k and plot the result by "scatter_cluster" function in the "helpers" package located at "./src/package/helpers"

In [10]:
# clustering the optimal value of k=3
plot_3, prediction_3=scatter_cluster(3, df_market_scaled, ["price_change_percentage_24h", "price_change_percentage_7d"])
In [11]:
# clustering the optimal value of k=4 
plot_4, prediction_4=scatter_cluster(4, df_market_scaled, ["price_change_percentage_24h", "price_change_percentage_7d"])
In [12]:
# clustering the optimal value of k=5 
plot_5, prediction_5=scatter_cluster(5, df_market_scaled, ["price_change_percentage_24h", "price_change_percentage_7d"])
In [13]:
# create copy of df_market_scaled and print pridiction results for each k
df_copy = df_market_scaled.copy()
df_copy = df_copy[["price_change_percentage_24h", "price_change_percentage_7d"]]

# add a new column to the DataFrame with the predicted clusters
predictions = [prediction_3, prediction_4, prediction_5]
for i,prediction in enumerate(predictions):      
    df_copy["k_"+str(i+3)] = predictions[i]

# print df_copy head
df_copy
Out[13]:
price_change_percentage_24h price_change_percentage_7d k_3 k_4 k_5
coin_id
bitcoin 0.508529 0.493193 1 3 1
ethereum 0.185446 0.934445 1 3 1
tether 0.021774 -0.706337 1 1 4
ripple -0.040764 -0.810928 1 1 4
bitcoin-cash 1.193036 2.000959 1 3 1
binancecoin 0.891871 1.327295 1 3 1
chainlink 0.011397 2.572251 1 3 1
cardano 0.102530 1.508001 1 3 1
litecoin 0.077497 0.334297 1 3 4
bitcoin-cash-sv 0.448952 -0.190684 1 1 4
crypto-com-chain 0.331280 -1.614844 1 1 0
usd-coin 0.034352 -0.733026 1 1 4
eos 0.155710 -0.922491 1 1 4
monero 0.262723 1.792602 1 3 1
tron 0.130050 -0.041018 1 1 4
tezos -0.151583 0.708196 1 3 4
okb -0.923203 -1.437359 1 1 0
stellar -0.277543 -0.385209 1 1 4
cosmos -0.255978 1.840274 1 3 1
cdai 0.180851 -0.704931 1 1 4
neo 0.286546 -0.326301 1 1 0
wrapped-bitcoin 0.515453 0.461843 1 3 1
leo-token 0.051758 -0.928381 1 1 0
huobi-token -0.052032 -0.457229 1 1 4
nem -0.217984 -0.849381 1 1 4
binance-usd 0.061339 -0.706669 1 1 4
iota 0.259097 0.249508 1 1 4
vechain 0.585089 -0.994231 1 1 0
zcash -0.127467 0.929119 1 3 1
theta-token -1.612188 -1.682027 1 1 0
dash -0.296940 0.094763 1 1 4
ethereum-classic -0.071312 -0.229484 1 1 4
ethlend -4.981042 -0.045178 2 0 3
maker -0.125168 0.580730 1 3 4
havven -1.428574 -0.025510 1 1 0
omisego 1.919812 0.370447 1 1 0
celsius-degree-token 1.045530 -0.618328 0 2 2
ontology -0.409044 -0.906963 1 1 0
ftx-token 0.414711 0.414044 1 1 4
true-usd 0.078038 -0.687745 1 1 4
digibyte 1.217453 -0.607714 1 1 0
Observation
Upon analyzing the scatter plots of the dataset for different values of k (i.e., k=3, k=4, and k=5), it appears that k=4 is the most suitable option. This is because the scatter plot with k=3 displays a substantial amount of data that remains unclustered, while the scatter plot with k=5 shows a significant overlap between two of the clusters. Therefore, the scatter plot with k=4 seems to provide the most meaningful and accurate clustering solution for this dataset.
3.3. Optimize Clusters with Principal Component Analysis.
In [14]:
# Create column names for the PCA components
pca_columns = ['PCA{}'.format(i) for i in range(1, 4)]

# Perform PCA on the scaled data and create a DataFrame with the results
pca = PCA(n_components=3)
market_pca = pca.fit_transform(df_market_scaled)
market_pca_df = pd.DataFrame(market_pca, columns=pca_columns, index=df_market_data.index)

# Display the first few rows of the DataFrame
market_pca_df.head()
Out[14]:
PCA1 PCA2 PCA3
coin_id
bitcoin -0.600667 0.842760 0.461595
ethereum -0.458261 0.458466 0.952877
tether -0.433070 -0.168126 -0.641752
ripple -0.471835 -0.222660 -0.479053
bitcoin-cash -1.157800 2.041209 1.859715
In [15]:
# retrieve the explained variance to determine how much information 
print(f"pca explained for first 3 components out of 7: {[f'{v:.2f}' for v in pca.explained_variance_ratio_[:3]]}")

# total explained variance with 3 components
print(f"total explained variance with 3 components: {sum(pca.explained_variance_ratio_[:3]):.2f}")

pca explained for first 3 components out of 7: ['0.37', '0.35', '0.18']
total explained variance with 3 components: 0.90
Observation

The principal component analysis (PCA) of our data indicates that the first three principal components account for approximately 90% of the total variance in the data. The first principal component explains around 37% of the variance, the second explains approximately 35%, and the third explains about 18%. Therefore, if we were to discard the other four components, we would only lose 10% of the variance in the data.

4.3. Find the Best Value for k Using the PCA Data.

Clustering the optimal value of k and plot the result by "scatter_cluster" function in the "helpers" package located at "./src/package/helpers"

In [16]:
# determine the optimal value of k by "clusters_methods" function in the "helpers" package located at "./src/package/helpers" is 
cluster_results_pca, optimal_ks_pca = clusters_methods(market_pca_df, ["wcss_elbow", "silhouette", "calinski_harabasz"])

# plotting methods by "score_plot" function in the "helpers" package located at "./src/package/helpers"
score_plot(cluster_results_pca, optimal_ks_pca)
Observation

After analyzing the data and evaluating the elbow method plot, it appears that k=4 could be the optimal number of clusters as the WCSS change starts to level off. However, the silhouette score suggests k=3 as the best choice, while the Calinski-Harabasz index is highest for k=10. Since the Calinski-Harabasz index may not work well for finding the best k in PCA situations, selecting the ideal number of clusters is subjective and requires domain knowledge and discretion, with k=3 and k=4 being reasonable options.

5.3. Cluster Cryptocurrencies with K-means Using the PCA Data.

Clustering the optimal value of k and plot the result by "scatter_3d_cluster" function in the "helpers" package located at "./src/package/helpers"

In [17]:
# clustering the optimal value of k=3
pca_plot_3, pca_prediction_3 = scatter_3d_cluster(3, market_pca_df, ['PCA1', 'PCA2', 'PCA3'])
In [18]:
# clustering the optimal value of k=4
pca_plot_4, pca_prediction_4 = scatter_3d_cluster(4, market_pca_df, ['PCA1', 'PCA2', 'PCA3'])
In [19]:
# create copy of market_pca_df and print pridiction results for each k
df_pca_copy = market_pca_df.copy()

# add a new column to the DataFrame with the predicted clusters
predictions = [pca_prediction_3, pca_prediction_4]
for i,prediction in enumerate(predictions):      
    df_pca_copy["k_"+str(i+3)] = predictions[i]

# display sample data
df_pca_copy
Out[19]:
PCA1 PCA2 PCA3 k_3 k_4
coin_id
bitcoin -0.600667 0.842760 0.461595 1 1
ethereum -0.458261 0.458466 0.952877 1 1
tether -0.433070 -0.168126 -0.641752 1 0
ripple -0.471835 -0.222660 -0.479053 1 0
bitcoin-cash -1.157800 2.041209 1.859715 1 1
binancecoin -0.516534 1.388377 0.804071 1 1
chainlink -0.450711 0.517699 2.846143 1 1
cardano -0.345600 0.729439 1.478013 1 1
litecoin -0.649468 0.432165 0.600303 1 1
bitcoin-cash-sv -0.759014 -0.201200 -0.217653 1 0
crypto-com-chain -0.248198 -1.376252 -1.462026 1 0
usd-coin -0.438408 -0.175337 -0.663388 1 0
eos -0.693425 -0.473815 -0.527597 1 0
monero 0.060499 2.909404 1.498571 1 1
tron -0.393352 -0.108192 -0.012756 1 0
tezos -0.796176 -0.494409 1.082812 1 1
okb 0.064075 -1.269825 -1.098829 1 0
stellar -0.489015 -0.732719 -0.062543 1 0
cosmos -0.306272 0.703415 1.714224 1 1
cdai -0.513528 -0.142802 -0.656566 1 0
neo -0.362120 -0.986914 -0.728752 1 0
wrapped-bitcoin -0.604265 0.827398 0.439316 1 1
leo-token -0.413296 -0.674115 -1.076628 1 0
huobi-token -0.407483 -0.212507 -0.351426 1 0
nem 0.608974 0.563532 -1.148742 1 0
binance-usd -0.450211 -0.151019 -0.647401 1 0
iota -0.764665 -0.517886 0.204990 1 0
vechain -0.556315 -1.938209 -1.261776 1 0
zcash -0.425147 0.492976 1.058048 1 1
theta-token 2.676868 -0.013954 -1.965207 1 0
dash -0.613923 -0.479337 0.339565 1 0
ethereum-classic -0.579924 -0.356334 -0.114942 1 0
ethlend 8.089018 -3.896891 2.301382 2 2
maker -0.389045 0.165041 0.379414 1 1
havven 0.865762 -2.261882 0.275583 1 0
omisego 0.111675 0.428316 -1.205398 1 0
celsius-degree-token 4.792395 6.767679 -1.986985 0 3
ontology -0.632355 -2.108117 -0.652227 1 0
ftx-token -0.593142 0.021485 0.209911 1 0
true-usd -0.458131 -0.135734 -0.635284 1 0
digibyte -0.297910 -0.191126 -0.909602 1 0
Observation

Upon analyzing the scatter plots of the dataset for different values of k (i.e., k=3, k=4), it seems that k=4 is the optimal choice. This is because the scatter plot with k=3 shows a significant amount of unclustered data, indicating that k=3 might not be sufficient for this dataset

4. Conclusion

In conclusion, our analysis of the dataset suggests that k=4 is the most suitable number of clusters for this dataset, as supported by the elbow method plot, silhouette score, and scatter plot analysis. While the Calinski-Harabasz index may not work well for PCA situations, k=3 and k=4 are still reasonable options. The top three principal components account for approximately 90% of the total variance, and clustering by fewer components results in more well-defined clusters. Plotting the resulting clusters on the principal component analysis clarifies the separation between the second and third clusters, which were initially overlapped in the full feature plot. However, clustering by fewer components also loses focus on specific timeframes of interest. Ultimately, selecting the ideal number of clusters is subjective and requires domain knowledge and discretion.

References

  1. Št’astný, T.; Koudelka, J.; Bílková, D.; Marek, L. Clustering and Modelling of the Top 30 Cryptocurrency Prices Using Dynamic Time Warping and Machine Learning Methods. Mathematics 2022, 10, 3672. https://doi.org/10.3390/math10193672
  2. Data for this dataset was generated by edX Boot Camps LLC, and is intended for educational purposes only.