Anomaly Detection via Randomized LU Decomposition
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Solution Overview
Problem
Current anomaly detection methods in high-dimensional big data are computationally intensive and often fail to detect unknown anomalies in real-time, leading to potential operational malfunctions and security threats, as they rely on rules, signatures, and domain expertise, making them ineffective against new or unknown attacks.
Innovation Solution
The implementation of a randomized LU decomposition method that reduces the dimensionality of high-dimensional data using orthogonal permutation matrices, enabling automatic and unsupervised classification of anomalies without requiring domain knowledge or predefined patterns, allowing for real-time detection of unknown undesirable events.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If rule-based anomaly detection methods are used, then detection accuracy for known anomalies is improved, but the system becomes computationally intensive and ineffective against unknown attacks
Solution Approach 1:
The patent transforms the anomaly detection problem by changing the parameter space from high-dimensional raw data to a low-dimensional subspace defined by the dictionary matrix D. This dimensionality reduction fundamentally alters the computational parameters, enabling fast projection-based anomaly scoring while maintaining detection effectiveness for both known and unknown anomalies.
Solution Approach 2:
The patent replaces the mechanical rule-based detection system with a data-driven matrix decomposition approach. Instead of applying complex rules and signatures to high-dimensional data, the system uses randomized LU decomposition to create a compact dictionary representation, substituting computational mechanics with a more efficient mathematical transformation.
2Speed
If real-time anomaly detection is implemented, then response time to undesirable events is improved, but computational complexity increases making it infeasible for high-dimensional data
Solution Approach 1:
The patent segments the anomaly detection process into two distinct phases: an offline training phase that performs computationally intensive randomized LU decomposition to build the dictionary, and an online detection phase that performs fast matrix projections. This segmentation allows complex computations to be done once beforehand, enabling real-time detection with minimal computational complexity.
Solution Approach 2:
The patent performs preliminary action by pre-computing the dictionary matrix D and its inverse through randomized LU decomposition during an offline training phase. This preliminary computation stores the essential structure of normal data patterns, so that during real-time operation, only simple projection operations are needed, dramatically reducing online computational complexity.
3Adaptability or versatility
If unsupervised anomaly detection is used, then adaptability to unknown anomalies is improved, but the system requires automatic classification without domain knowledge
Solution Approach 1:
The patent implements self-service by enabling the system to automatically learn and adapt to unknown anomaly patterns without requiring domain expertise or manual rule configuration. The randomized LU decomposition automatically discovers the intrinsic structure of normal data, creating a dictionary that inherently captures what constitutes normal behavior, allowing the system to autonomously detect deviations.
Solution Approach 2:
The patent creates a universal anomaly detection framework that can handle various types of high-dimensional data (network traffic, sensor data, financial transactions) without requiring data-specific rules or domain knowledge. The matrix decomposition approach provides a unified methodology that adapts to different data types and anomaly patterns through a single general-purpose algorithm.
Data Source
AI summary
Detection of abnormalities in HDBD is performed by processing it to obtain a dictionary from a training data. This is done by computing a low rank randomized LU decomposition which enables constant online updating of the training data and thus gets constant updating of the normal profile in the background.