A Gaussian Multivariate Hidden Markov Model for Breast Tumor Diagnosis

Abstract

The stage of a tumor is sometimes hard to predict, especially early in its development. The size and complexity of its observations are the major problems that lead to false diagnoses. Even experienced doctors can make a mistake in causing terrible consequences for the patient. We propose a mathematical tool for the diagnosis of breast cancer. The aim is to help specialists in making a decision on the likelihood of a patient’s condition knowing the series of observations available. This may increase the patient’s chances of recovery. With a multivariate observational hidden Markov model, we describe the evolution of the disease by taking the geometric properties of the tumor as observable variables. The latent variable corresponds to the type of tumor: malignant or benign. The analysis of the covariance matrix makes it possible to delineate the zones of occurrence for each group belonging to a type of tumors. It is therefore possible to summarize the properties that characterize each of the tumor categories using the parameters of the model. These parameters highlight the differences between the types of tumors.