[Paper Review] Randomized LU decomposition: An Algorithm for Dictionaries Construction

Aviv Rotbart, Gil Shabat+2 more|arXiv (Cornell University)|Feb 17, 2015

Algorithms and Data Compression22 references3 citations

TL;DR

This paper proposes a fast, scalable, and memory-efficient dictionary construction algorithm based on randomized LU decomposition for low-rank matrix factorization of training data. It enables under-complete dictionary learning that simplifies classification, outperforms SVD in speed and memory use, and achieves high accuracy in content-based file type detection—even with minimal file fragments—demonstrating strong performance in digital security applications like identifying malicious code in PDFs.

ABSTRACT

In recent years, distinctive-dictionary construction has gained importance due to his usefulness in data processing. Usually, one or more dictionaries are constructed from a training data and then they are used to classify signals that did not participate in the training process. A new dictionary construction algorithm is introduced. It is based on a low-rank matrix factorization being achieved by the application of the randomized LU decomposition to a training data. This method is fast, scalable, parallelizable, consumes low memory, outperforms SVD in these categories and works also extremely well on large sparse matrices. In contrast to existing methods, the randomized LU decomposition constructs an under-complete dictionary, which simplifies both the construction and the classification processes of newly arrived signals. The dictionary construction is generic and general that fits different applications. We demonstrate the capabilities of this algorithm for file type identification, which is a fundamental task in digital security arena, performed nowadays for example by sandboxing mechanism, deep packet inspection, firewalls and anti-virus systems. We propose a content-based method that detects file types that neither depend on file extension nor on metadata. Such approach is harder to deceive and we show that only a few file fragments from a whole file are needed for a successful classification. Based on the constructed dictionaries, we show that the proposed method can effectively identify execution code fragments in PDF files. $ extbf{Keywords.}$ Dictionary construction, classification, LU decomposition, randomized LU decomposition, content-based file detection, computer security.

Motivation & Objective

• Address the need for efficient, scalable dictionary construction methods in data processing and classification tasks.
• Overcome limitations of existing methods like SVD in speed, memory usage, and scalability, especially for large or sparse datasets.
• Develop a generic, parallelizable dictionary construction framework applicable across diverse applications.
• Enable robust, content-based file type identification independent of file extensions or metadata.
• Demonstrate the method’s effectiveness in detecting execution code fragments in files such as PDFs, relevant to computer security.

Proposed method

• Apply randomized LU decomposition to perform low-rank matrix factorization on training data, enabling efficient dictionary learning.
• Use the randomized LU decomposition to generate an under-complete dictionary, simplifying both training and classification processes.
• Leverage the numerical stability and computational efficiency of randomized algorithms to handle large-scale and sparse matrices.
• Construct dictionaries directly from raw data without relying on metadata or file extensions.
• Utilize the resulting dictionary for signal classification by projecting new signals onto the learned subspace.
• Ensure the method is parallelizable and memory-efficient, suitable for real-time or large-scale deployment.

Experimental results

Research questions

• RQ1 Can randomized LU decomposition outperform traditional SVD in speed, memory usage, and scalability for dictionary construction?
• RQ2 How effective is the resulting under-complete dictionary in enabling accurate classification of unseen signals?
• RQ3 To what extent can content-based file type detection be achieved without relying on file extensions or metadata?
• RQ4 How few file fragments are required for reliable classification using the proposed dictionary-based method?
• RQ5 Can the method detect embedded execution code fragments in files like PDFs with high accuracy?

Key findings

• The randomized LU decomposition method is significantly faster and more memory-efficient than SVD, especially for large and sparse matrices.
• The constructed dictionaries are under-complete, simplifying both dictionary learning and signal classification.
• The method achieves high accuracy in content-based file type detection using only a few file fragments, reducing reliance on full file content.
• The approach successfully identifies execution code fragments in PDF files, demonstrating utility in digital security contexts.
• The algorithm is scalable and parallelizable, making it suitable for real-time or large-scale data processing applications.
• The method performs well on sparse data, which is common in file content representation, outperforming traditional SVD in such settings.