Aerosol time-of-flight mass spectrometry data analysis: a benchmark of clustering algorithms

Airborne particulate matter is an important component of atmospheric pollution, affecting human health, climate, and visibility. Modern instruments allow single particles to be analyzed one-by-one in real time, and offer the promise of determining the sources of individual particles based on their mass spectral signatures. The large number of particles to be apportioned makes clustering a necessary step. The goal of this study is to compare using mass spectral data the accuracy and speed of several clustering algorithms: ART-2a, several variants of hierarchical clustering, and K-means. Repeated simulations with various algorithms and different levels of data preprocessing suggest that hierarchical clustering methods using derivatives of Ward's algorithm discriminate sources with fewer errors than ART-2a, which itself discriminates much better than point-wise hierarchical clustering methods. In most cases, K-means algorithms do almost as well as the best hierarchical clustering. These efficient algorithms (clustering derived from Ward's algorithm, ART-2a and K-means) are most accurate when the relative peak areas have been pre-scaled by taking the square root. Analysis times vary within a factor of 30, and when accuracy above 95% is required, run times scale up as the square of the number of particles. Algorithms derived from Ward's remain the most accurate under a wide range of conditions and conversely, for an equal accuracy, can deliver a shorter list of clusters, allowing faster and maybe on-the-fly classification.