[pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

Author: pre-commit-ci[bot]

machine_learning/gaussian_mixture_model.py

@@ -85,7 +85,9 @@ def _m_step(self, X, responsibilities):
 
         for k in range(self.n_components):
             diff = X - self.means_[k]
-            self.covariances_[k] = (responsibilities[:, k][:, np.newaxis] * diff).T @ diff
+            self.covariances_[k] = (
+                responsibilities[:, k][:, np.newaxis] * diff
+            ).T @ diff
             self.covariances_[k] /= Nk[k]
             # Add small regularization term for numerical stability
             self.covariances_[k] += np.eye(n_features) * 1e-6
@@ -155,4 +157,4 @@ def plot_results(self, X):
     gmm = GaussianMixture(n_components=3, max_iter=100, seed=42)
     gmm.fit(X)
     labels = gmm.predict(X)
-    gmm.plot_results(X)
+    gmm.plot_results(X)