Master thesis : Optimization and machine learning techniques in flow cytometry

Abstract

This study is based on two previous studies: ’Clustering and Kernel Density Estimation for Assessment of Measurable Residual Disease by Flow Cytometry’ and Comparison of Three Contour Gating Methods in Flow Cytometry. These two studies aimed to identify suspicious clusters of AML (Acute Myeloid Leukemia) patient cells using different clustering techniques. The contour lines of the clusters are ellipsoids. A cluster is suspicious if it presents a large abnormality ratio (AR1). The data of the cells are obtained using Multiparameter Flow Cytometry (MFC). These data require a logicle transformation to be usable by cytometrist. After the LT, it has been observed that the data distribution tends to be a multivariate normal distribution (MND). The graphical representations of the PDF (probability density function) of MND are ellipsoids. Hence, if it is possible to improve the MND of the data resulting from the LT, it would be very appropriate to use ellipsoids as contour lines to determine the cluster since the graphical representation of the PDF of an MND is an ellipsoid. The first part of the study is to optimise the parameters of the LT to improve the MND of the data. It has been proved that it was possible to optimise the LT parameters. A normality test: the Agostino test is used to quantify the normality of the set to determine which combination of the parameters gives the best MND of the set. The second part of this study is to identify new potential clustering techniques. Two usual clustering methods are proposed: the Gaussian mixture method and the k-means. In addition, two methods, Gap statistic and the silhouette coefficient, that determine in how many clusters the data set must be divided are introduced. These methods estimate the optimal number of clusters and could help the cytometrist in tagging the suspicious clusters. The techniques have been tested in terms of AR and computation time. The best techniques are k-means and the silhouette coefficient. However, the clustering techniques proposed in the previous studies and paragraphs do not optimise the clusters’ contour lines to maximise the AR. So, the problem is written as an optimisation problem (OP). The OP objective is to maximise the AR by updating the contour lines of the clusters. The formulation of the problem is non-convex and discrete. It is impossible to solve it in a decent time. After approximating the discrete problem in a continuous problem, the gradient descent is used to solve the continuous OP. The results conclude that this clustering technique optimises the cluster’s contour lines to maximise the AR. Finally, the initial OP is reformulated and solved. It gives very good results in terms of AR. However, the the computation time of this formulation is too large to be used in practical applications. The two initial objectives of this study are full-filled. First, it has been proven that it is possible to optimise the LT parameters to improve the MND of the data set. Then, the problem has been formulated as an optimisation problem that maximises the AR. A technique, gradient descent, manages to solve such an OP.