Fuzzy C-Means Clustering: A Review of Applications in Breast Cancer Detection

Abstract

This paper reviews the potential use of fuzzy c-means clustering (FCM) and explores modifications to the distance function and centroid initialization methods to enhance image segmentation. The application of interest in the paper is the segmentation of breast tumours in mammograms. Breast cancer is the second leading cause of cancer deaths in Canadian women. Early detection reduces treatment costs and offers a favourable prognosis for patients. Classical methods, like mammograms, rely on radiologists to detect cancerous tumours, which introduces the potential for human error in cancer detection. Classical methods are labour-intensive, and, hence, expensive in terms of healthcare resources. Recent research supplements classical methods with automated mammogram analysis. The basic FCM method relies upon the Euclidean distance, which is not optimal for measuring non-spherical structures. To address these limitations, we review the implementation of a Mahalanobis-distance-based FCM (FCM-M). The three objectives of the paper are: (1) review FCM, FCM-M, and three centroid initialization algorithms in the literature, (2) illustrate the effectiveness of these algorithms in image segmentation, and (3) develop a Python package with the optimized algorithms to upload onto GitHub. Image analysis of the algorithms shows that using one of the three centroid initialization algorithms enhances the performance of FCM. FCM-M produced higher clustering accuracy and outlined the tumour structure better than basic FCM.

Keywords: biogeography-based optimization algorithm; firefly algorithm; fuzzy c-means clustering; genetic algorithm; image segmentation; mammogram.

Figure 1

(${\mathit{A}}_{\mathit{0}}$) Initial image. (${\mathit{B}}_{\mathit{0}}$) Salt and pepper noise. (${\mathit{C}}_{\mathit{0}}$) Gaussian noise. (${\mathit{D}}_{\mathit{0}}$) Uniform noise. (${\mathit{A}}_{\mathit{1}}$–${\mathit{A}}_{\mathit{8}}$): Euclidean-distance-based fuzzy c-means clustering (FCM-EU), Euclidean-distance-based biogeography-based optimization (FCM-EU-B), Euclidean-distance-based firefly algorithm (FCM-EU-F), Euclidean-distance-based genetic algorithm (FCM-EU-GA), Mahalanobis-distance-based fuzzy c-means clustering (FCM-M), Mahalanobis-distance-based biogeography-based optimization (FCM-M-B), Mahalanobis-distance-based firefly algorithm (FCM-M-F), and Mahalanobis-distance-based genetic algorithm (FCM-M-GA), for (${\mathit{A}}_{\mathit{0}}$). Similar for (${\mathit{B}}_{\mathit{1}}$–${\mathit{B}}_{\mathit{8}}$), (${\mathit{C}}_{\mathit{1}}$–${\mathit{C}}_{\mathit{8}}$), and (${\mathit{D}}_{\mathit{1}}$–${\mathit{D}}_{\mathit{8}}$) and for (${\mathit{B}}_{\mathit{0}}$), (${\mathit{C}}_{\mathit{0}}$), and (${\mathit{D}}_{\mathit{0}}$), respectively.

Figure 2

(A) Initial image. (B) Euclidean-distance-based fuzzy c-means clustering (FCM-EU). (C) Euclidean-distance-based biogeography-based optimization (FCM-EU-B). (D) Euclidean-distance-based firefly algorithm (FCM-EU-F). (E) Euclidean-distance-based genetic algorithm (FCM-EU-GA). (F) Mahalanobis-distance-based fuzzy c-means clustering (FCM-M). (G) Mahalanobis-distance-based biogeography-based optimization (FCM-M-B). (H) Mahalanobis-distance-based firefly algorithm (FCM-M-F). (I) Mahalanobis-distance-based genetic algorithm (FCM-M-GA).