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Efficient Quantum One-Class Support Vector Machines for Anomaly Detection Using Randomized Measurements and Variable Subsampling

Michael Kölle, Afrae Ahouzi, Pascal Debus, Elif Çetiner, Robert Müller, Daniëlle Schuman, Claudia Linnhoff-Popien

TL;DR

This work tackles the quadratic-time bottleneck of quantum OC-SVMs for anomaly detection by integrating randomized measurements kernels with variable subsampling ensembles and rotating feature bagging. The proposed VS-RFB-RM approach achieves linear time in both dataset size and feature/qubit count while delivering higher average precision, albeit with high variance. Empirical results on synthetic and credit-card fraud datasets show substantial training/testing speedups and improved detection performance, illustrating a favorable scalability-accuracy trade-off. The study also outlines directions for further enhancement, including more ensemble components, alternative feature maps, and comparisons with additional kernel-approximation techniques.

Abstract

Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large datasets. In recent work, quantum randomized measurements kernels and variable subsampling were proposed, as two independent methods to address this problem. The former achieves higher average precision, but suffers from variance, while the latter achieves linear complexity to data size and has lower variance. The current work focuses instead on combining these two methods, along with rotated feature bagging, to achieve linear time complexity both to data size and to number of features. Despite their instability, the resulting models exhibit considerably higher performance and faster training and testing times.

Efficient Quantum One-Class Support Vector Machines for Anomaly Detection Using Randomized Measurements and Variable Subsampling

TL;DR

This work tackles the quadratic-time bottleneck of quantum OC-SVMs for anomaly detection by integrating randomized measurements kernels with variable subsampling ensembles and rotating feature bagging. The proposed VS-RFB-RM approach achieves linear time in both dataset size and feature/qubit count while delivering higher average precision, albeit with high variance. Empirical results on synthetic and credit-card fraud datasets show substantial training/testing speedups and improved detection performance, illustrating a favorable scalability-accuracy trade-off. The study also outlines directions for further enhancement, including more ensemble components, alternative feature maps, and comparisons with additional kernel-approximation techniques.

Abstract

Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large datasets. In recent work, quantum randomized measurements kernels and variable subsampling were proposed, as two independent methods to address this problem. The former achieves higher average precision, but suffers from variance, while the latter achieves linear complexity to data size and has lower variance. The current work focuses instead on combining these two methods, along with rotated feature bagging, to achieve linear time complexity both to data size and to number of features. Despite their instability, the resulting models exhibit considerably higher performance and faster training and testing times.
Paper Structure (51 sections, 15 equations, 5 figures)

This paper contains 51 sections, 15 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. One-Class Support Vector Machines
  4. Quantum Kernel Embedding
  5. Related Work
  6. Quantum Anomaly Detection
  7. Efficient Gram Matrix Evaluation
  8. Approach
  9. Randomized Measurements Kernel
  10. Variable Sampling Ensembles using Inversion Test Kernels
  11. Variable Subsampling Ensembles using Randomized Measurements Kernels
  12. Variable Subsampling Ensembles with Rotated Feature Bagging using Randomized Measurements Kernels
  13. Experimental Setup
  14. Datasets
  15. The Synthetic Data
  16. ...and 36 more sections

Figures (5)

  • Figure 1: The linearly inseparable points on the input space are mapped using a quantum feature map $\Phi$ into a feature space where they are linearly separable aggarwal2017introduction.
  • Figure 2: Quantum circuits for IQP-like feature map, inversion test and swap test
  • Figure 3: The protocol and the circuit architecture for calculating quantum kernel functions using randomized measurement.kölle2024efficient
  • Figure 4: The mean and standard deviation bars for the performance of the OC-SVM models trained using the methods presented. Column (a) represents the results for the synthetic data (2 features). Column (b) shows the results for the Credit Card Fraud data (6 features). Column (c) corresponds to the experiments with 500 points and varying feature numbers.
  • Figure 5: Training and testing times in seconds, based on the data size in columns (a) and (b), and on feature/qubit numbers in column (c).