1. Classifying Overlapping Data by Combining Meta Learners and Bayesian Networks
Akbar Akbari Esfahani1, Theodor Asch2
University of Colorado Denver1, USGS – Crustal Geophysics and Geochemistry Science Center1,2,
Abstract
Training site and Data Acquisition
Results from the Training Site
The US Department of Defense is interested in classifying types of unexploded ammunition versus clutter at the Aberdeen Proving Grounds, MD. To this end, a hybrid model using numerical inversion and Kohonen’s Self Organizing Maps (SOM) [1]. While the hybrid approach has been successful, the numerical inversion is computationally intensive and thus time consuming. To overcome this problem, I use a single neural network model that combines meta learners with Bayesian Networks to achieve a acceptable accuracy and be computational tractable. So far the combinations of Dagging with a BayesNet algorithm classifies the ammunition 99.9% correctly. The training and testing of the network model is done in less than 30 seconds versus the 3 week period of the numerical inversion.
Confusion Matrix of Results
There are 6 types of ordinances and clutter dispersed thru out the field. ALLTEM is an on-time time-domain EM system that uses a continuous triangle-wave excitation to measure the target-step response rather than traditional impulse response. The system multiplexes through three orthogonal transmitting loops and records a total of different transmitting and receiving loop combinations with a spatial data sampling interval of 20 cm
Time to train network model: About 1 sec.
Time to perform a 10-fold cross validation on data: about 14 sec.
Time for complete Model building: ~ 15 sec.
Conclusion
The Network
We can train a model in approximately 15 seconds with 100% accuracy.
Data used on the Neural Net model is the field generated time series.
To train and test on a blind set, the time requirement is less then 30 seconds and can be performed by almost any field laptop.
Dagging:
Dagging uses stratified folds of the training [2], [3]. According to literature Dagging is particularly useful when building classifiers that have poor time complexity in terms of the number of readings.
BayesNet:
Bayesian networks refer to directed acyclic graphical models[4], a probabilistic graphical model that represents a set of random variables and their dependencies. Bayesian network represent the probabilistic relationship between cause and effect. Given the effects, the network computes the probabilities of various causes to the effects presented. The learning algorithm for Bayesian Network consists of two parts: an evaluation function of a given network based on the data and a search algorithm that searches through the space of possible networks. The K2 algorithm [5] was chosen as the evaluation function. It starts with an ordering of the attributes and processes each node then in turn using a greedy algorithm to consider adding edges from previously processed nodes to the current one. With each step, it adds the edge that maximizes the network’s score based on AIC statistics. Once a node cannot be refined any further, the algorithm moves to the next node. Next the searching algorithm estimates conditional probability tables of the network, directly from the data, once the structure of the network has been learned by the K2 algorithm.
Goals and Objectives
Distinguish clutter from ordinance.
Discover an algorithm for real time field application.
Algorithm should not rely on input from the inversion model.
Network performance suitable for field.
(Time < 5min)
Future Application
The algorithm remains to be tested in the field on a blind data set where a scoring can be assigned.
References
The Mathematical Problem
[1] Friedel, M. J., Asch, T., & Oden, C. (2012). Hybrid analysis of multi-axis electromagnetic data for discrimination of munitions and explosives of concern. Geophysical Journal International.
[2] Tang, K. M., & Witten, I. H. (1997). Stacking Bagged and Dagged Models. Fourteenth international Conference on Machine Learning (pp ). San Francisco: Morgan Kaufmann Publishers Inc.
[3] Breiman, L. (1994). Bagging Predictors, Technical Report No Berkeley: University of California Berkeley.
[4] Witten, I. H., Frank, E., & Hall, M. A. (2011). Data Mining: Practical Machine Learning Tools and Techniques, 3rd Edition. Burlington, MA: Morgan Kaufmann.
[5] Cooper, G. F., & Herskovits, E. (1992). A Bayesian Method for the Induction of Probabilistic Networks from Data. Machine Learning, 9,
11 of the 13 independent variables of the data set are collinear
Variable 1
Variable 2
Variable 3 - 9
Variable 10
Variable 11 1
0.997
Variable 3
0.995
0.999
1, … , 1
Variable
-0.947
-0.957
0.973, … ,
-0.922
-0.933
-0.935, … , 0.982
0.983