# Robust Support Vector Data Description with Truncated Loss Function for Outliers Depression

## TL;DR

This paper improves the SVDD model for anomaly detection by introducing a truncated loss function framework, making it more robust to outliers and mislabeled data.

## Contribution

A novel truncated loss function framework is introduced for SVDD, along with three new truncated loss functions and a fast ADMM algorithm for solving them.

## Key findings

- The proposed truncated loss functions show superior robustness against outliers in synthetic and real-world datasets.
- The fast ADMM algorithm efficiently solves various truncated loss functions and ensures convergence.
- The new SVDD models outperform existing models in terms of generalization and noise handling.

## Abstract

Support vector data description (SVDD) is widely regarded as an effective technique for addressing anomaly detection problems. However, its performance can significantly deteriorate when the training data are affected by outliers or mislabeled observations. This study introduces a universal truncated loss function framework into the SVDD model to enhance its robustness and employs the fast alternating direction method of multipliers (ADMM) algorithm to solve various truncated loss functions. Moreover, the convergence of the fast ADMM algorithm is analyzed theoretically. Within this framework, we developed the truncated generalized ramp, truncated binary cross entropy, and truncated linear exponential loss functions for SVDD. We conducted extensive experiments on synthetic and real-world datasets to validate the effectiveness of these three SVDD models in handling data with different noise levels, demonstrating their superior robustness and generalization capabilities compared to other SVDD models.