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Distribution-based Low-rank Embedding

Bardia Yousefi

TL;DR

This work tackles the challenge of extracting dominant temporal thermal patterns from infrared breast thermography for very early cancer detection. It introduces two novel LD embedding strategies—James-Stein for eigenvectors (JSE) and Weibull embedding—and integrates them into a low-rank thermography framework to derive thermomics suitable for classifier training. Empirical results show that JSE improves leading-basis estimation and that Weibull embedding preserves heterogeneity, with maximum cross-validated accuracies reaching around 81.7%. The approach yields a noninvasive, cost-effective screening aid prior to mammography, supported by comparisons to existing low-rank and embedding methods and a focus on robust, HD-to-LD dimensionality reduction. Future work will enlarge the cohort and refine embedding strategies to further enhance diagnostic reliability.

Abstract

The early detection of breast abnormalities is a matter of critical significance. Notably, infrared thermography has emerged as a valuable tool in breast cancer screening and clinical breast examination (CBE). Measuring heterogeneous thermal patterns is the key to incorporating computational dynamic thermography, which can be achieved by matrix factorization techniques. These approaches focus on extracting the predominant thermal patterns from the entire thermal sequence. Yet, the task of singling out the dominant image that effectively represents the prevailing temporal changes remains a challenging pursuit within the field of computational thermography. In this context, we propose applying James-Stein for eigenvector (JSE) and Weibull embedding approaches, as two novel strategies in response to this challenge. The primary objective is to create a low-dimensional (LD) representation of the thermal data stream. This LD approximation serves as the foundation for extracting thermomics and training a classification model with optimized hyperparameters, for early breast cancer detection. Furthermore, we conduct a comparative analysis of various embedding adjuncts to matrix factorization methods. The results of the proposed method indicate an enhancement in the projection of the predominant basis vector, yielding classification accuracy of 81.7% (+/-5.2%) using Weibull embedding, which outperformed other embedding approaches we proposed previously. In comparison analysis, Sparse PCT and Deep SemiNMF showed the highest accuracies having 80.9% and 78.6%, respectively. These findings suggest that JSE and Weibull embedding techniques substantially help preserve crucial thermal patterns as a biomarker leading to improved CBE and enabling the very early detection of breast cancer.

Distribution-based Low-rank Embedding

TL;DR

This work tackles the challenge of extracting dominant temporal thermal patterns from infrared breast thermography for very early cancer detection. It introduces two novel LD embedding strategies—James-Stein for eigenvectors (JSE) and Weibull embedding—and integrates them into a low-rank thermography framework to derive thermomics suitable for classifier training. Empirical results show that JSE improves leading-basis estimation and that Weibull embedding preserves heterogeneity, with maximum cross-validated accuracies reaching around 81.7%. The approach yields a noninvasive, cost-effective screening aid prior to mammography, supported by comparisons to existing low-rank and embedding methods and a focus on robust, HD-to-LD dimensionality reduction. Future work will enlarge the cohort and refine embedding strategies to further enhance diagnostic reliability.

Abstract

The early detection of breast abnormalities is a matter of critical significance. Notably, infrared thermography has emerged as a valuable tool in breast cancer screening and clinical breast examination (CBE). Measuring heterogeneous thermal patterns is the key to incorporating computational dynamic thermography, which can be achieved by matrix factorization techniques. These approaches focus on extracting the predominant thermal patterns from the entire thermal sequence. Yet, the task of singling out the dominant image that effectively represents the prevailing temporal changes remains a challenging pursuit within the field of computational thermography. In this context, we propose applying James-Stein for eigenvector (JSE) and Weibull embedding approaches, as two novel strategies in response to this challenge. The primary objective is to create a low-dimensional (LD) representation of the thermal data stream. This LD approximation serves as the foundation for extracting thermomics and training a classification model with optimized hyperparameters, for early breast cancer detection. Furthermore, we conduct a comparative analysis of various embedding adjuncts to matrix factorization methods. The results of the proposed method indicate an enhancement in the projection of the predominant basis vector, yielding classification accuracy of 81.7% (+/-5.2%) using Weibull embedding, which outperformed other embedding approaches we proposed previously. In comparison analysis, Sparse PCT and Deep SemiNMF showed the highest accuracies having 80.9% and 78.6%, respectively. These findings suggest that JSE and Weibull embedding techniques substantially help preserve crucial thermal patterns as a biomarker leading to improved CBE and enabling the very early detection of breast cancer.
Paper Structure (15 sections, 16 equations, 5 figures, 4 tables)

This paper contains 15 sections, 16 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related works and Motivations
  3. Method
  4. Overview of Low-rank representation thermography
  5. Low-rank Embedding
  6. Weibull Embedding
  7. James--Stein for Eigenvectors Thermography
  8. Extracting thermomics, imaging biomarkers
  9. Results
  10. Study Population
  11. Results of JSE in thermography
  12. Results of Weibull embedding
  13. Thermomics and classification results
  14. Discussion
  15. Conclusions

Figures (5)

  • Figure 1: Scheme of thermography system setup for early detection of breast cancer leading abnormality. Breast cancer exerts a multifaceted influence on vasodilation, intricately linked to various factors. Angiogenesis factors, inflammatory mediators, hormones, nitric oxide, prostaglandins, and matrix metalloproteinases collectively orchestrate a complex interplay that modulates vascular responses, underscoring the intricate relationship between breast cancer and the dynamic regulation of blood vessel function in its microenvironment. Dynamic thermography has significant advantage over static thermography due to increase the chance of capturing temporal thermal fluctuations which can be used as a biomarker for very early diagnosis of breast cancer in the CBE stage.
  • Figure 2: Workflow of applying JSE with low-rank Weibull embedding in thermography.
  • Figure 3: Six examples of PCT versus JSE thermography results, three healthy cases (a-c) and three abnormal (d-f) cases. JSE unequivocally bolsters heterogeneous thermal pattern underlining for vasodilation in breast cancer cases.
  • Figure 4: Comparing PCT to Weibull embedding thermography results, we present six instances, three from healthy cases (a-c) and three from abnormal cases (d-f). The application of Weibull embedding significantly enhances the delineation of heterogeneous thermal patterns associated with vasodilation in breast cancer cases.
  • Figure 5: Reciever operating characteristic (ROC) curve of the model used for evaluation of Weibull-embedding thermal data for different matrix factorization techniques.

Theorems & Definitions (3)

  • Definition 1
  • Definition 2
  • Definition 3