Improved Aerosol Apportionment by Bayesian Classifier

1
Improved Aerosol Apportionment by Bayesian
Classifier Thomas Rebotier, Steve Toner and Kim
Prather, U.C. San Diego
INTRODUCTION Apportioning ambient aerosol
measured by ATOFMS is made by comparing their
mass spectra with seeds obtained from source
studies. Currently, matching depends on the dot
product between the particle spectrum and the
average spectrum of a particle class, the seed
(Song et al., 1999). An aerosol matches a class
when its dot product is larger than a given
vigilance factor (typically 0.8). This
approach ignores cluster size seeds obtained
from 5 particles pull as much weight as seeds
obtained from 2,000. Dot product matching also
ignores differences in variability ?(m/z) is
always larger for the peaks that have large m/z
on average, so that the existence of smaller
significant peaks is entirely swamped by noise on
larger peaks. For example, Na2Cl creates two
peaks (at 81 and 83) which very dependable
marks of fresh sea salt but their influence in
matching is nothing compared to that of the noise
from the large Na peak which occurs in fresh and
aged sea salt, as well as in biomass.

• METHODS
• Spectral Data Dual polarity spectra, m/Z up to
  350
• Aerosol Time-Of-Flight Mass Spectrometer
  (ATOFMS)
• Dynamometer Study originally
• 28 Light Duty Vehicles (LDVs) (Sodeman et al.,
  2005)
• 6 Heavy Duty Diesel Vehicles (HDDV) (Toner et
  al., 2005)
• Removing atypical vehicles (smokers,
  non-converter cars)
• Separate Vehicles for training and testing set.
• Clusters to Match the Data to from ART-2a, v.f.
  0.85
• Each subset vehicle type (LDV/HDV) was clustered
  separately, and the resulting clusters were
  collected, to make 2 sets Fine and UltraFine.
  Figure 1 shows the spread of the spectra for 8
  clusters in the Fine set, and the median spectrum
  of these clusters.
• Matching techniques compared
• Dot Product matching to nearest centroid
• Bayesian matching with independent normal
  distribution per peak (Full)
• Bayesian matching with one normal distribution
  for each cluster (Spherical)
• Bayesian matching with quartile-based box"
  distribution (the likelihood is a product of 1
  for peaks within the 2nd and third quartiles and
  0.5 for peaks outside)

DISCUSSION Overall Bayesian matching has a
higher percentage correct than nearest centroid
matching, but they have opposite biases.
Bayesian matching favors HDVs and dot product to
nearest centroid favors LDV. Why? Probably
because the LDV clusters have in average a
smaller diameter (as defined by their standard
deviation in spectral space).
The clusters have been binned according to the
standard deviation of the training set spectra
(those that defined the centroids). The figure
shows the fraction of test particles apportioned
into these bins. Bayesian matching tends to
match into wider clusters.
Bayesian matching was also expected to match more
particles into the clusters that originally
included more particles. (Because of the prior
in the Bayes equation).

RESULTS
Examples of clusters from HDVs (trucks) and LDVs
(cars). The most numerous, largest and smallest
clusters of are included. Above, a 2-dimensional
representation of how the individual spectral are
scattered in spectral space notice the
variations of cluster diameter. Below, the mass
spectra for M/Z1 to 100.
The clusters have been binned according to the
number of particles that defined them in the
training set. The figure shows the fraction of
test particles apportioned into these bins.
Bayesian matching tends to match into clusters
that originally were more numerous.
These problems can be addressed by a Bayesian
Classifier (Duda and Heart, 1973). In
particular, mixture of Gaussians in which each
spectral class is represented by a Gaussian
distribution in 700 dimensions (350 positive and
negative m/z). To match an unknown particle, its
likelihood is computed by the Gaussian formula,
then weighted by the prior probabilities (the
expected number of particles in each cluster).
The particle is apportioned to the class of
highest posterior probability.

• CONCLUSIONS
• Bayesian matching apportions particles with the
  desired bias for clusters that are initially
  wider and larger
• Overall, Bayesian gives a lower apportionment
  error than dot product matching to the nearest
  centroid. BUT
• Dot product matching apportions too many spectra
  to small clusters, resulting in a pro-LDV bias
• Bayesian matching apportions too many spectra to
  large clusters, resulting in a pro-HDV bias.
• Keywords Apportionment, Bayesian Classifier,
  Hierarchical Clustering, ART-2A
• REFERENCES
• Duda, R. O., and Hart, P. E. (1973). Pattern
  Classification, Wiley Interscience.
• Sodeman, D. A., Toner, S. M., and Prather, K. A.
  (2005).Determination of Single Particle Mass
  Spectral Signatures from Light Duty Vehicle
  Emissions, Environmental Science Technology, in
  press.
• Song, X.-H., Fergenson, D. P., Hopke, P. K., and
  Prather, K. A. (1999).Classification of Single
  Particles Analyzed by Atofms Using an Artificial
  Neural Network, Art-2a, Anal. Chem, 71 (4),
  860-865.
• Toner, S. M., Sodeman, D. A., and Prather, K. A.
  (2005).Single Particle Characterization of
  Ultrafine- and Fine-Mode Particles from Heavy
  Duty Diesel Vehicles Using Aerosol Time-of-Flight
  Mass Spectrometry, in preparation.

The Bayes formula
Assuming a normal (Gaussian) distribution, the
likelihood is
Comparing the distributions assumed by each
matching method. The mixture of Gaussians model
allows variations of shape and intensity.