def per_user_metrics(item_factors, URM_train, URM_test, k=10, max_users=500):
test_users = np.where(URM_test.getnnz(axis=1) > 0)[0]
if len(test_users) == 0:
return np.array([]), np.array([])
test_users = test_users[: min(max_users, len(test_users))]
hits_list = []
ndcgs = []
for u in test_users:
train_items = URM_train[u].nonzero()[1]
test_items = set(URM_test[u].nonzero()[1])
if len(train_items) == 0 or len(test_items) == 0:
continue
user_vec = item_factors[train_items].mean(axis=0)
scores = item_factors.dot(user_vec)
scores[list(train_items)] = -np.inf
top_k = np.argsort(-scores)[:k]
hit = 1.0 if any(i in test_items for i in top_k) else 0.0
hits_list.append(hit)
dcg = sum(
1.0 / np.log2(idx + 2)
for idx, item in enumerate(top_k)
if item in test_items
)
idcg = sum(
1.0 / np.log2(i + 2) for i in range(min(len(test_items), k))
)
ndcg = dcg / idcg if idcg > 0 else 0.0
ndcgs.append(ndcg)
return np.array(hits_list), np.array(ndcgs)
k_values = [5, 10, 15, 20, 30, 40]
hit_means = []
hit_sems = []
ndcg_means = []
ndcg_sems = []
for k in k_values:
hits, ndcgs = per_user_metrics(
item_factors,
user_rating_matrix_train,
user_rating_matrix_test,
k=k,
max_users=500,
)
if len(hits) == 0:
hit_means.append(0.0)
hit_sems.append(0.0)
ndcg_means.append(0.0)
ndcg_sems.append(0.0)
continue
hit_means.append(hits.mean())
hit_sems.append(
hits.std(ddof=1) / np.sqrt(len(hits)) if len(hits) > 1 else 0.0
)
ndcg_means.append(ndcgs.mean())
ndcg_sems.append(
ndcgs.std(ddof=1) / np.sqrt(len(ndcgs)) if len(ndcgs) > 1 else 0.0
)
fig, axes = plt.subplots(1, 2, figsize=(14, 4))
axes[0].errorbar(
k_values,
hit_means,
yerr=hit_sems,
marker="o",
linewidth=2,
markersize=8,
color="steelblue",
capsize=5,
)
axes[0].set_xlabel("k (number of recommendations)")
axes[0].set_ylabel("Hit Rate")
axes[0].set_title("Hit Rate@k Performance (with SEM)")
axes[0].grid(alpha=0.3)
axes[1].errorbar(
k_values,
ndcg_means,
yerr=ndcg_sems,
marker="s",
linewidth=2,
markersize=8,
color="coral",
capsize=5,
)
axes[1].set_xlabel("k (number of recommendations)")
axes[1].set_ylabel("NDCG")
axes[1].set_title("NDCG@k Performance (with SEM)")
axes[1].grid(alpha=0.3)
plt.tight_layout()
plt.show()
