Reconstruction Error

INFO

Measures the difference between original data and reconstructed data, often used in dimensionality reduction methods like PCA and autoencoders.

How It Works

For input $x$ and its reconstruction $\hat{x}$:

$$\text{Reconstruction Error}=\frac{1}{n}\sum _{i=1}^n{\Vert x_i-{\hat{x}}_i\Vert }^2$$

• $x_i$: Original data point
• ${\hat{x}}_i$: Reconstructed data point
• $n$: Number of samples

This metric captures how well the model preserves the original structure.

What to Look For

• Lower error = better reconstruction
• Useful for Anomaly Detection and compression quality
• Can be visualized as residual maps or error histograms

Application Models

• Principal Component Analysis (PCA)
• Autoencoders