Energy Efficiency — Multi-target Regression

The Energy Efficiency dataset (768 samples, 8 building-design features, 2 continuous targets) is a multi-target regression problem: each building has a Heating Load and a Cooling Load. This tutorial trains one SOM on the 8 features, then projects each target separately onto that same map to show how a single SOM supports multi-target analysis.

Note

Full runnable notebook: notebooks/energy_efficiency.ipynb. The figures below are its outputs.

1. Load and standardize the data

The first 8 columns are building-design features; the last two columns are the targets (Heating Load, then Cooling Load). The BMU search compares raw feature distances, so standardizing the features is essential.

import torch
import pandas as pd
from sklearn.preprocessing import StandardScaler

# energy_efficiency.csv ships in the repo
df = pd.read_csv("data/notebooks/energy_efficiency.csv")

feature_cols = df.columns[:8]
features = torch.tensor(
    StandardScaler().fit_transform(df[feature_cols].values), dtype=torch.float32
)
heating = torch.tensor(df["Heating Load"].values, dtype=torch.float32)
cooling = torch.tensor(df["Cooling Load"].values, dtype=torch.float32)

2. Train the SOM

from torchsom import SOM

som = SOM(
    x=25,
    y=15,
    num_features=features.shape[1],
    epochs=100,
    batch_size=16,
    sigma=1.45,
    learning_rate=0.95,
    neighborhood_order=3,
    topology="rectangular",
    initialization_mode="pca",
    random_seed=42,
)
som.initialize_weights(data=features, mode=som.initialization_mode)
q_errors, t_errors = som.fit(data=features)

3. Check convergence

from torchsom import SOMVisualizer

viz = SOMVisualizer(som=som)
viz.plot_training_errors(
    quantization_errors=q_errors, topographic_errors=t_errors
)
Energy efficiency training curve

Both errors fall and flatten — training is long enough.

4. Inspect the map structure

The U-matrix exposes cluster boundaries; the hit map shows where the data lands.

viz.plot_distance_map(
    distance_metric=som.distance_fn_name,
    neighborhood_order=som.neighborhood_order,
)
viz.plot_hit_map(data=features)
Energy efficiency U-matrix Energy efficiency hit map

5. Heating load landscape

Build the BMU→sample map once, then reuse it for every target. Here it colors each neuron by the mean heating load of its samples, and by the standard deviation.

bmus_map = som.build_map("bmus_data", data=features)
viz.plot_metric_map(
    bmus_data_map=bmus_map,
    data=features,
    target=heating,
    reduction_parameter="mean",
)
viz.plot_metric_map(
    bmus_data_map=bmus_map,
    data=features,
    target=heating,
    reduction_parameter="std",
)
Heating load mean map Heating load standard deviation map

The mean map shows heating load varying smoothly across the grid, so nearby neurons hold buildings with similar loads. The std map reveals where the target is consistent: low values mark neurons whose samples share nearly the same heating load.

6. Cooling load landscape

The same bmus_map is reused — no retraining and no rebuild — now projecting the cooling load onto the identical map.

viz.plot_metric_map(
    bmus_data_map=bmus_map,
    data=features,
    target=cooling,
    reduction_parameter="mean",
)
viz.plot_metric_map(
    bmus_data_map=bmus_map,
    data=features,
    target=cooling,
    reduction_parameter="std",
)
Cooling load mean map Cooling load standard deviation map

Heating and cooling loads produce similar but not identical landscapes on the same map: the two targets are correlated yet diverge in regions where building geometry affects them differently. The std map again marks where the cooling load is consistent within each neuron.

Next steps