Fuzzy Entropy Classification Systems and Their Application to Mass Spectrometry of the Proteome

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Fuzzy Entropy Classification Systems and Their
Application to Mass Spectrometry of the Proteome

• Peter de B. Harrington, Ping Chen, and Mariela
  Ochoa

Ohio University Center for Intelligent Chemical
Instrumentation Department of Chemistry and
Biochemistry Athens, OH 45701-2979
Peter.Harrington_at_Ohio.edu
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Rule-Building Expert Systems

• In the 1980s expert systems were a promising
  technology except for the knowledge acquisition
  bottleneck
• It was hard to find expertise for solving most
  problems
• When an expert was found, it was difficult to
  take their knowledge and encode it in a logical
  system.
• Rule-building expert systems solved this problem
  by using machine learning to construct logical
  rules from exemplary sets of data

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Classification Trees and Inductive Logic

• Logical rules may be implemented efficiently in a
  tree structure with general rules at the root of
  the tree and precise rules at the nodes.

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Multivariate Rules

• Multivariate rules may be obtained simply by
  using a linear discriminant that furnishes a
  logic. These systems were prevalent in the 1970s
  and 1980s as linear learning machines or
  perceptrons.

Jurs, P. C. Kowalski, B. R. Isenhour, T. L.,
Computerized Learning Machines Applied to
Chemical Problems - Investigation of Convergence
Rate and Predictive Ability of Adaptive Binary
Pattern Classifiers. Analytical Chemistry 1969,
41, 690-695.
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Information Regarding Classes

• Use a binary encode matrix Y.
• Each row corresponds to a spectrum as a row of X.
• The columns designate a class.
• Summation of the columns gives the number of
  spectra in each class.

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Multivariate Fuzzy Rules

• A simple rule is obtained from a weight vector w
  that is orthogonal to a (n-1) dimensional
  hyperplane which separates the spectra X. The
  attribute a defines the intersection of the
  hyperplane and the weight vector.

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Fuzzy Rules
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Optimizing the Rule Using Fuzzy Entropy

• The weight w and attribute a of the rule are
  adjusted so that the entropy of classification is
  minimized.
• The temperature t is constrained so that the
  first derivative is maximized.

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Optimal Fuzziness

• The computational temperature parameter scales
  the magnitude of the weight vector.
• The optimal temperature is the one that maximizes
  the first derivative of the classification
  entropy H(Cw,a,t)X,Y with respect to
  temperature.
• This criterion speeds up training using gradient
  methods by maintaining a steep response surface.
• The response is continuous between clusters.

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Nonlinearly Separable Data
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Divide and Conquer
The nonlinearly separable problem can be divided
into smaller linearly separable sets of data.
This division can be accomplished using
artificial neural networks or classification
trees.
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Classification Trees and Inductive Logic
Logical rules may be implemented efficiently in a
tree structure with general rules at the root of
the tree and precise rules at the nodes.
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MALDI as a Soft Ionization Method

• Introduced by Karas and Hillenkamp (1987) as
  ionization method for non-volatile polar
  biological and organic macromolecules and
  polymers
• Low concentration of analyte uniformly dispersed
  in solid or liquid matrix
• Matrix should have strong absorbance at laser
  excitation wavelength and low sublimation
  temperature
• Three main processes occur formation of solid
  solution, matrix excitation, and analyte
  ionization

Karas, M. Bachmann, D. Bahr, U. Hillenkamp, F.
Int. J. Mass Spectrom. Ion Process. 1987, 78,
53-68.
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MALDI Mechanism and TOF-MS Instrumentation
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Schematic of a Linear Time-of-Flight Mass
Spectrometer Used in MALDI
UV (337 nm)
Microchannel plate detector
Field-free drift zone
Source
Pulse voltage
Analyte/matrix
Ed 0
Length D
Length s
Backing plate (grounded)
Extraction grid (source voltage -Vs)
Detector grid -Vs
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M_at_ldi-LRTM Mass Spectrometer Time-of-Flight by
Micromass (UK)

• Instrumental parameters
• Laser Nitrogen UV (337 nm)
• Firing rate 5 Hz
• 10 shots/spectrum
• Laser pulse energy 1.2 x 10-4 J
• Spot width 100 mm
• Ion optics Linear TOF path length 0.7 m
• Ion source Grounded time lag focusing source
  (delayed extraction) 500 ns
• Accelerating voltage 15 kV
• Detector Fast dual micro-channel plate (MCP)

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Mass Alignment Using a Second Order Polynomial to
the Average Spectrum
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Escherichia Coli Experimental Design
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Principal Component Analysis

• Decomposition into orthogonal matrices C and S
• The matrices maximize variance
• The matrices are abstract in that they do not
  represent physical or chemical trends

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Latin-Partitions for Evaluating Classifiers

• The Latin-partition method is used to randomly
  divide a data set into training-prediction set
  pairs.
• A specified number of pairs are obtained so that
  the every spectrum in the data set is used once
  and only once for prediction.
• The partitioning maintains the same proportions
  of class memberships in the training and
  prediction sets.
• Replicate spectra of the same samples are never
  split between training and prediction sets.

C. Wan and P.B. Harrington, Screening GC-MS
data for carbamate pesticides with
temperature-constrained-cascade correlation
neural networks Analytica Chimica Acta 408
(2000) 1-12.
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Latin Partitions
A
B
C
A
A
B
C
B
C
A
Prediction Set
A
B
A
B
A
B
A
C
C
C
B
C
C
B
Training Set
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Table 1. Confusion Matrix from 50x2 Latin
Partitions with 95 Confidence Intervals
Before model building principal component
compression was used so that the number of
variables was 250. The principal components were
re-calculated for every Latin-partition. These
same components were used for prediction.
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Table 2. Confusion Matrix from 50x2 Latin
Partitions with 95 Confidence Intervals. Tree
Built with Average Spectra and Evaluated with
Average Spectra
Table 3. Confusion Matrix from 50x2 Latin
Partitions with 95 Confidence Intervals. Tree
Built with Average Spectra and Evaluated with
Average Spectra
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FuRES Rule 1
ANOVA-PCA
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Concluding Thoughts

• FuRES trees can give good prediction even when
  training sets contain data of questionable
  quality.
• Using individual spectra gives improved
  prediction (significance level P0.08), although
  at a cost of longer computation times
• Classification trees are amenable to
  interpretation and can be used to disclose the
  location of biomarkers

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Acknowledgements

• Students
• Ping Chen Lisa Stout
• Preshious Rearden Leanna Kishler
• Yao Lu Abby Berg
• National Institutes of Health
• Mental Health
• Child Health and Human Development
• Federal Aviation Administration - Donation of a
  Barringer Ionscan 350
• Ion Track Instruments for Support and Donation of
  the Itemizer 2 and VaporTracer 1
• Sionex for the donation of DMS
• U.S. Army EBCB - GeoCenters Donation of 4
  Chemical Agent Monitors and Funding
• Research Opportunity Award-Research Corporation
• Wright-Patterson Air Force Base-INNSSI Fuel
  Analysis