import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from numerapi import NumerAPI

# import kmeans from sklearn
from sklearn.cluster import KMeans

np.random.seed(42)
napi = NumerAPI()

napi.download_dataset("numerai_training_data.parquet", "data/numerai_training_data.parquet")
trainset = pd.read_parquet("data/numerai_training_data.parquet")
feature_names = [f for f in trainset.columns if "feature_" in f]

2022-01-07 17:43:43,733 INFO numerapi.utils: target file already exists
2022-01-07 17:43:43,734 INFO numerapi.utils: download complete

After the release of the new dataset feature groups went away, making it more difficult to work with. Feature groups similar to the old data can be recreated using k-means clustering. Below is a correlation matrix of the new dataset. The only decernable pattern here is that every ~200 features is similar in some way.

# generate feature correlation matrix
# use 10000 rows to reduce computation time
all_feature_corrs = trainset[feature_names].sample(10000 ,random_state = 0).corr()

# take the absolute value of the correlation matrix. 
# inveresely correlated features are assumed to be related.
all_feature_corrs = all_feature_corrs.abs()

#plot correlation matrix
plt.figure(figsize=(20,20))
fig = plt.imshow(all_feature_corrs)
plt.title("Feature Correlation Matrix")
plt.plasma()
plt.colorbar(fig)
plt.show()

We can use k-means clustering on the columns of the correlation matrix to cluster them together. Each column shows how a given feature is correlated with all of the others. We want 2 features with similar columns to be in the same group.

# cluster all feature corrs using kmeans into clusters
N_CLUSTERS = 24
kmeans = KMeans(n_clusters=N_CLUSTERS)
kmeans.fit(np.transpose(all_feature_corrs.values))
print(kmeans.labels_.shape)

# list of lists of feature names
feature_groups = []
for i in range(N_CLUSTERS):
    feature_group = []
    for j, name in enumerate(feature_names):
        if kmeans.labels_[j] == i:
            feature_group.append(name)

    feature_groups.append(feature_group)

# concatenate all feature groups into one list, effectively ordering them by group
ordered_feature_names = []
for i, group in enumerate(feature_groups):
    ordered_feature_names = ordered_feature_names + group

(1050,)

The new feature groups can be visualized by reordering columns in the dataset by group, and recalculating its correlation matrix. The bright squares along the diagonal of the matrix below show the new groups and how features interact within them.

# generate feature correlation matrix with a now ordered feature list
# use 10000 rows to reduce computation time
ordered_feature_corrs = trainset[ordered_feature_names].sample(10000 ,random_state = 0).corr()
ordered_feature_corrs = ordered_feature_corrs.abs()

#plot correlation matrix
plt.figure(figsize=(20,20))
fig = plt.imshow(ordered_feature_corrs)
plt.title("Feature Correlation Matrix with Sorted Feature Names")
plt.plasma()
plt.colorbar(fig)
plt.show()

Notice that the repeating pattern seen in the original correlation matrix shows up in each group. We can do better by repeating this method recursively. Basically finding sub groups within the new groups.

# generate feature groups. then recursivly generate feature groups with the new feature groups
def recursive_feature_grouping(df, feature_names, n_clusters, depth = 1):
    if depth == 0 or len(feature_names) <= n_clusters:
        return feature_names

    # cluster all feature corrs using kmeans into clusters
    kmeans = KMeans(n_clusters=n_clusters)
    kmeans.fit(df[feature_names].corr().abs().values)

    feature_groups = []
    for i in range(n_clusters):
        feature_group = []
        for j, name in enumerate(feature_names):
            if kmeans.labels_[j] == i:
                feature_group.append(name)

        feature_groups.append(
            recursive_feature_grouping(df, feature_group, n_clusters, depth=depth-1,)
        )

    return feature_groups

# turn nested list (tree) into reordered feature list like before
def tree_to_list(tree):
    output_list = []

    def traverse(node):
        if isinstance(node, list):
            for item in node:
                traverse(item)
        else:
            output_list.append(node)

    traverse(tree)

    return output_list

feature_tree = recursive_feature_grouping(
    trainset.sample(10000), feature_names, n_clusters=5, depth=6
)
ordered_feature_names = tree_to_list(feature_tree)

The recursive method produces a more interesting looking correlation matrix

# generate feature correlation matrix with a now ordered feature list
# use 10000 rows to reduce computation time

ordered_feature_corrs = trainset[ordered_feature_names].sample(10000 ,random_state = 0).corr()
ordered_feature_corrs = ordered_feature_corrs.abs()
plt.figure(figsize=(20,20))
fig = plt.imshow(ordered_feature_corrs)
plt.title("Feature Correlation Matrix with Sorted Feature Names using Recursive Feature Grouping")
plt.plasma()
plt.colorbar(fig)
plt.show()

Below is code for turning the nested list of groups (tree) into a dataframe.

# return df with feature names, and thier path in the tree
# holy recursion, batman!
def tree_to_df(tree, n_clusters):
    df = pd.DataFrame({
        "feature_names": tree_to_list(tree)
    }).set_index("feature_names")
    
    # records the path of each feature in the tree
    path = []

    def traverse(node, depth = 0):
        if isinstance(node, list):
            for i, item in enumerate(node):
                path.append(i)
                traverse(item, depth+1)
                path.pop()
        else:
            # in this case node is a feature name (leaf)
            for i, item in enumerate(path):
                col_name = "depth_{}".format(i+1)
                if col_name not in df.columns:
                    df[col_name] = np.nan
                df.loc[node, col_name] = item
    traverse(tree)

    depth_cols = [c for c in df.columns if "depth_" in c]
    
    # prune columns with nans
    for col in depth_cols:
        if df[col].isnull().max():
            df.drop(col, axis=1, inplace=True)
        
    depth_cols = [c for c in df.columns if "depth_" in c]

    # give each group a number according to its path in the tree
    for i, c in enumerate(depth_cols):
        df[c] = df[c].astype(int)
        if i < len(depth_cols) - 1:
            df[depth_cols[i+1]] = (df[c] * n_clusters) + df[depth_cols[i+1]]

    # add 1 to every element
    for i, c in enumerate(depth_cols):
        df[c] = df[c] + 1

    return df

group_df = tree_to_df(feature_tree, n_clusters=5)
group_df.to_csv("feature_groups.csv")
tree_to_df(feature_tree, n_clusters=5)

	depth_1	depth_2	depth_3	depth_4
feature_names
feature_generative_honorific_tughrik	1	1	1	1
feature_biased_puzzling_cessation	1	1	1	1
feature_sludgiest_telltale_mutant	1	1	1	1
feature_palatalized_unsucceeded_induration	1	1	1	1
feature_fishiest_simulatory_roadholding	1	1	1	1
...	...	...	...	...
feature_coalier_typhoid_muntin	5	25	124	616
feature_bold_brindle_playground	5	25	124	617
feature_mailed_harried_grant	5	25	124	618
feature_forworn_hask_haet	5	25	124	619
feature_illiterate_stomachal_terpene	5	25	125	621

1050 rows × 4 columns

Feature groups get more granular at each depth

# visualize feature groups at various depths

import plotly.express as px
import plotly.io as pio
pio.renderers.default='notebook'

depth_cols = [c for c in group_df.columns if "depth_" in c]
for col in depth_cols:
    group_df[col] = (len(group_df) / (group_df[col].max() + 1)) * (group_df[col] + 1)
    group_df[col] = group_df[col].astype(int)

group_df.head()

fig = px.imshow(group_df, aspect='auto', color_continuous_scale=px.colors.sequential.Turbo)
fig.show()

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