Accurately identifying and extracting clusters from atom probe tomography (APT) reconstructions is extremely challenging, yet critical to many applications. Currently, the most prevalent approach to detect clusters is the maximum separation method, a heuristic that relies heavily upon parameters manually chosen by the user. In this work, a new clustering algorithm, Gaussian mixture model Expectation Maximization Algorithm (GEMA), was developed. GEMA utilizes a Gaussian mixture model to probabilistically distinguish clusters from random fluctuations in the matrix. This machine learning approach maximizes the data likelihood via expectation maximization: given atomic positions, the algorithm learns the position, size, and width of each cluster. A key advantage of GEMA is that atoms are probabilistically assigned to clusters, thus reflecting scientifically meaningful uncertainty regarding atoms located near precipitate/matrix interfaces. GEMA outperforms the maximum separation method in cluster detection accuracy when applied to several realistically simulated data sets. Lastly, GEMA was successfully applied to real APT data.

X-ray fluorescence (XRF) microscopy is an important tool for studying trace metals in biology, enabling simultaneous detection of multiple elements of interest and allowing quantification of metals in organelles without the need for subcellular fractionation. Currently, analysis of XRF images is often done using manually defined regions of interest (ROIs). However, since advances in synchrotron instrumentation have enabled the collection of very large data sets encompassing hundreds of cells, manual approaches are becoming increasingly impractical. We describe here the use of soft clustering to identify cell ROIs based on elemental contents, using data collected over a sample of the malaria parasite Plasmodium falciparum as a test case. Soft clustering was able to successfully classify regions in infected erythrocytes as “parasite,” “food vacuole,” “host,” or “background.” In contrast, hard clustering using the k-means algorithm was found to have difficulty in distinguishing cells from background. While initial tests showed convergence on two or three distinct solutions in 60% of the cells studied, subsequent modifications to the clustering routine improved results to yield 100% consistency in image segmentation. Data extracted using soft cluster ROIs were found to be as accurate as data extracted using manually defined ROIs, and analysis time was considerably improved.