This document discusses a study that used classificatory decomposition and multi-objective evolutionary algorithms to classify protein LIBS spectra. Classificatory decomposition breaks down LIBS spectra into basis functions and coefficients to reconstruct the original signals while minimizing reconstruction error and classification error. The researchers used a leave-one-out approach where a single LIBS instance is left out of training and used to test the classification scheme, which is repeated for all instances. Their results found an average reconstruction error of around 0.2 and an 80% reduction, and their classification scheme performed as either correct or incorrect.

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Classification of LIBS Spectra using Classificatory Decomposition
Leave-One-Out Approach
Kofi Forson , Kyrhee Powell, and Tomasz Smolinski
Department of Computer and Information Sciences, Delaware State University, Dover DE 19901, USA
What is LIBS?
Laser Induced Breakdown Spectroscopy (LIBS) is a technique that provides
information about the chemical components of a sample through laser ablation.
Different methods have been applied to classify protein LIBS data. Some of
these proteins include Bovine Serum Albumin, Opsteopontin, Leptin, and
Insulin-like Growth Factor II. The classification of these particular proteins can
lead to the detection of diseases, including ovarian cancer.
Classificatory Decomposition
Classificatory Decomposition (CD) is a form of signal decomposition that also
provides classification awareness. It breaks down signals, such as LIBS spectra,
into basis functions. Basis functions are elements that can be found in all of the
original signals, and coefficients are utilized to scale the basis functions to
reconstruct the original signals.
An example of classificatory decomposition involving signals can be seen below:
Figure 1: Example of signal decomposition: A) The original datasets. B) The underlying basis functions. C) The
coefficients for representation of the original signals in the new attribute space.
The main objectives of classificatory decomposition and this experiment are:
• To minimize the reconstruction error of the data;
• To minimize the number of basis functions needed to reconstruct the data;
• To minimize the classification error.
Leave-One-Out Approach
The Leave-One-Out (LOO) approach involves taking a single instance out,
training the classifier on the remaining instances, and then testing the
classification scheme on the instance that was taken out. The process is repeated
n times, where n is the number of instances in the input dataset, and the average
accuracy measure over n trials determines the overall goodness of the classifier.
Methodology
To generate the batches of data used for training the classification scheme, we
employed several Python scripts. One of the essential Python scripts we uti-
lized extracted the LIBS data, created new documents, and input the batches in
the newly created documents with corresponding parameter and test files. In to-
tal, there were 132 batches of LIBS data, on which we trained our classification
scheme.
A fundamental component of our classification scheme and experiment involved
Multi-Objective Evolutionary Algorithms (MOEA), such as end-VEGA,
which we implemented in C++. MOEAs mimic the principles of evolution and
natural selection to optimize multiple objectives simultaneously to arrive at a set
of potential solutions to a given optimization problem.
The figure below explains the evolutionary loop process:
Figure 2: A schematic of an evolutionary algorithm.
Methodology (continued)
After training the classification scheme on the LIBS data, we evaluated the ac-
curacy of our classification scheme by utilizing Weka. Weka is a software work-
bench that incorporates several standard machine learning techniques, which al-
low a user to further analyze a large body of data.
Figure 3: Sample plots for each of the four protein classes.
Our experimental settings consisted of:
• A population size of 20 individuals in the MOEA;
• A generation count of 100;
• 132 batches of LIBS spectra;
• 9 trials testing the accuracy of reconstruction and classification.
Results
When running the test trials on the 132 batches of LIBS spectra, the reconstruc-
tion error was almost always below 1. The average reconstruction error was
around 0.2. Moreover, the reduction on average was about 80 percent.
Furthermore, when classifying the LIBS spectra using Weka, our result was ei-
ther right or wrong. We either got a 0 for an incorrect classification or a 1 for a
correct classification.
Forthcoming Research/Conclusions
In the future, we would like to:
• Train different classification schemes on the LIBS spectra;
• Utilize additional MOEAs in our classification schemes;
• Expand the use of classificatory decomposition to different kinds of data.
Furthermore, we learned that the Leave-One-Out Approach has disadvantages
when it comes to the classification of data, because it is either hit or miss. We re-
ceived a 0 for an incorrect classification or a 1 for a correct classification.
References
• Sparse Correlation Kernel Analysis and Evolutionary Algorithm-Based Model-
ing of the Sensory Activity within the Rats Barrel Cortex
• Evolutionary Algorithms and Rough Sets-Based Hybrid Approach to Classifi-
catory Decomposition of Cortical Evoked Potentials
• Independent Component Analysis-motivated Approach to Classificatory De-
composition of Cortical Evoked Potentials
• Hybridization of Independent Component Analysis, Rough Sets, and Multi-
Objective Evolutionary Algorithms for Classificatory Decomposition of Cor-
tical Evoked Potentials
• Detection of unusual trajectories using multi-objective evolutionary algorithms
and rough sets
Acknowledgments
We acknowledge the Optical Science Center for Applied Research (OSCAR),
the financial support of The National Science Foundation (NSF-CREST grant
No 1242067 and of the National Aeronautics and Space Administration (NASA
URC 5 grant No NNX09AU90A).