Classification of buried underwater objects is challenging owing to several issues ..... the training stage a very straightforward procedure. Although this one-pass ...
Proceedings of International Joint Conference on Neural Networks, Orlando, Florida, USA, August 12-17, 2007
Buried Underwater Object Classification Using Multi-Aspect Classifier
a
Collaborative
Jered Cartmill, Mahmood R. Azimi-Sadjadi, and Neil Wachowski Abstract- In this paper, a new collaborative multi-aspect classification system (CMAC) is introduced. CMAC utilizes a group of collaborative decision-making agents capable of producing a high-confidence final decision based on features obtained over multiple aspects. This system is then applied to a buried underwater target classification problem. The results show that CMAC provides excellent multi-ping classification of mine-like objects while simultaneously reducing the number of false alarms compared to a multi-ping decision-level fusion classifier.
I. INTRODUCTION
Classification of buried underwater objects is challenging owing to several issues that include: variability of target signatures and features with respect to the incidence angle and range of the sonar, the presence of competing natural and man-made clutter, surface and bottom reverberation effects, and lack of any a priori knowledge about the shape and geometry of abundant non-mine-like objects that can be encountered. Furthermore, variations in the environmental conditions add even more difficulty to this problem. In order to overcome these challenges, it is desirable to devise feature extraction and target classification methodologies that remain robust with respect to these conditions. In real-life situations, a decision about the presence and type of object is made based upon the observation of the properties of the received signals over several sonar pings. Typically, two general approaches are used to perform multiping classification. In the first approach, features are extracted across multiple pings in order to characterize common signatures that indicate if an object has mine-like or nonmine-like properties. This can be accomplished using canonical correlation analysis (CCA) [1], which extracts coherencebased features from pairs of sonar returns. Using these features, successful discrimination between mine-like and non-mine-like objects have been reported [2], [3]. The second approach is based upon designing classification schemes that exploit information from multiple sonar pings. This can be performed using either decision-level [4] or featurelevel fusion [5] mechanisms. In decision-level fusion [4], intermediate decisions obtained using a single-ping classifier are fused to yield a final decision. A disadvantage of the decision-level fusion is its inability to use a variable number of pings when making a final decision, rendering it unsuitable for use in real mine-hunting applications. Moreover, the cost Jered Cartmill, Neil Wachowski, and Mahmood R. Azimi-Sadjadi are with the Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523-1373, USA. E-mail: azimi oengr.colostate.edu
function used by the decision-level fusion system does not allow for collaboration in the decision-making process amongst the decision making agents responsible for producing the intermediate decisions, hence resulting in a loss of potentially valuable information. In feature-level fusion [5], the class of an object is chosen based on the corresponding sequence of features obtained from an object over multiple pings. Hidden Markov model (HMM) is used in conjunction with a neural network to perform multi-aspect feature-level classification fusion. The advantage of feature-level fusion is its ability to classify a variable number of pings. However, this system can be very difficult to train if a limited amount of data is available, or when a large variety of mine-like and non-minelike objects are involved. The development of a system capable of performing multiping classification using a group of collaborative decision making agents can overcome the problems with the aforementioned systems. The main idea is to share information regarding preliminary decisions in order to reach a highconfidence final decision. The development of such a system for use in the buried underwater object classification problem is precisely the goal of this paper. II. A COLLABORATIVE MULTI-ASPECT CLASSIFIER
SYSTEM In this section, a new classification system known as a collaborative multi-aspect classifier (CMAC) is introduced. This system utilizes a set of collaborating agents that communicate with each other prior to making a final decision. The development of the CMAC system is motivated by its collaborative ability to minimize a cost function based on overall misclassifications. This property is not shared by any of the other fusion-based multi-ping classifiers [4], [5]. This system is inspired from Varshney's work [6], [7] for developing a system capable of performing distributed detection in sensor networks using distributed data fusion
(DDF).
A. Structure of CMAC In the proposed CMAC system (shown in Fig. 1), a group of N decision-making agents is used to produce N separate decisions regarding N pattern vectors (observations) xi, 1,... N. This is accomplished in the following manner. First, an agent i,whose internal structure is shown in Fig. 2, makes a preliminary decision, designated by ui, using a twoclass probabilistic neural network (PNN) [8] based on the pattern available to the agent. The purpose of this preliminary decision is to assist the other N -1 agents in making their
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jth Agent
Fig. 1. Proposed CMAC system (N
=
Fig. 2. Internal Structure of the ith decision agent.
3 case).
final decisions. These preliminary decisions are chosen to be continuous-valued scalars whose values vary between zero and one, and are designed to represent the confidence of an agent regarding the class of the feature vector. Each agent shares this information with other agents in the group using a "coordinator," whose function is to facilitate the sorting and transmission of the appropriate preliminary decisions to and from each agent. Upon the receipt of ui's, i 1, .... N, the coordinator creates N vectors denoted uir, e [1, n], where Uir
=
[U1, U.1,~Ui-:
Ui+l: ...
UN]
( (1)
Note that the index term ir is used to denote that this vector will be "received" by the ith agent for use in its final decision computation. Once these vectors are formed, the coordinator subsequently transmits each to the appropriate agent's BPNN probability estimator (shown in Fig. 2), whose function is to estimate the class conditional probability terms needed for calculating the threshold used in the final decision by each agent. This is discussed in more detail in the subsequent section. Next, each agent makes a final decision based on a likelihood ratio involving both its feature vector xi, and the evidence (in the form of the preliminary decisions) provided by the other N -1 agents in the group. A combining scheme is also included to fuse the N final decisions made by the N agents and produce a single final classification decision based on the sequence of N pings. This allows the results of the CMAC system to be directly compared to the results
produced using other multi-ping fusion classifiers [4], [5].
B. Final Decision Rule Formulation In order to determine the optimal final decision rule for each agent, our goal is to minimize the overall expected cost of misclassification for each agent. Several assumptions are made in our formulation. The first assumption is that the set of input vectors {xi,i = 1, ... N} are conditionally independent random vectors given the class Ck, that is, N
p(Xl,**
XN
Ck) J7Jp(xiCk), tl1
(2)
where p(xijCk) is the a priori class conditional probability. We also assume that based only on its observation xi, the ith agent makes a single local preliminary decision ui, i.e.,
Ui = Yi(xi)
(3)
Here, the decision ui is a preliminary decision made by the ith decision maker whose purpose is to help the other N -1 1,... N; j :t i. To agents produce final outputs ufj, J obtain a final decision ufi, a decision rule -yfi(ui) is used such that Uf i
=
(4)
Yfi (Xi: Uir),
where Uir,i C [1, n] denotes the set of preliminary decisions used by the ith agent's fusion center obtained from the coordinator. The cost incurred in making the classification decision ufi=m for the ith agent is denoted by Jmk, where k is the true class, m, k C {0, 1}. We assume that the cost of making an incorrect classification is greater than the cost of making a correct classification, i.e., Jm=n
k
> Jm=k k
(5)
me {O,1};n C {O,1};k C {O,1}.
Also, we assume that P(Uf i
=
°|U$r, i
=
l =
0, xi) >
1, ~... , N;I
=
°Ur, ui 1, . .. , N; 1I + i
P(Uf
i =
1
xi)
(6) where u$r is equivalent to uir without its Ith element ul. Essentially, (6) implies that when the final decision made by the ith agent is compared to the preliminary decision made by the Ith agent, it is more likely that the decisions will agree than disagree. This makes sense, as it is logical to assume that preliminary decision made by the Ith agent should influence the final decision made by the ith agent. Using these assumptions, the problem is to obtain the optimum strategies 'Yf>i = 1,... N. That is, we wish to determine the final decision rule that minimizes the expected cost of making a misclassification for each of the agents, i.e., min E[J{yfi(xi, Uir), Ck}] subject to (2)-(6).
(7)
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Solving (7) leads to the following optimal decision rules associated with the ith agent, i = 1, . . ., N. At the ith agent's data fusion center, the final decision ufi is produced using the decision rule 'fy, i 1,... N, which is obtained using a likelihood ratio test given by Ufi
=
A(xi) A):
(8)
tfi
Ufi
where the threshold
1
tfi(u6))
=
0
is obtained by (see Appendix
N
p(Uj C0)
P(Co) I tfi(Uir)
[Jii
Jool
JNJ
=
P (Cl)
l
j= . , .
p(uj CO IJo
Jill
where Jm,k denotes the cost of choosing the mth class (m C {0, 1}) when the true class was k, k C {0, 1}. In this equation, the dependence on uir is implicitly assumed because the distribution of the preliminary decisions i is directly obtained using the uj, j = 1,... , N;j elements of uir. Here, A(xi) is obtained via a likelihood ratio, i.e., 0) A(xi) p(x Cl ) as will be shown in the subsequent section. Clearly, we notice that to generate the final decision ufi 1,1 ... , N, for each agent, one needs to compute A(xi) and tfi(Uir). The latter term requires the outputs of a BPNN trained to estimate the conditional distribution of the preliminary decisions (assumed to be the same for all agents), and is discussed in Section II-D. The former term, A(xi), requires only the PNN outputs, and is discussed in the next section.
C. PNN-Based Preliminary Classification Decision Maker The original PNN structure consists of three feedforward layers, the input layer, pattern layer, and summation layer [8]. Feature vectors are applied to the input layer, which passes them to each neuron in the pattern layer. The pattern layer consists of K pools of pattern neurons, where K is the number of classes. In each pool k, k = 1, . . . , K, there are Nk pattern neurons, each of which represents exactly one pattern from the training set for class Ck. For the input feature vector x, the output of each pattern neuron is
f (X; w kU) or): .
Nkc (27r)d/2,7d
EC N
(x
-w())T(X-w
)
where w(j) is the weight vector of the jth neuron in the kth pool, and the nonlinear function f (.) represents the activation functions of the neurons. In the summation layer, the kth , K, forms the weighted sum of all the neuron, k = 1, outputs from the kth pool in the pattern layer. For the "0-1" cost function and a uniform a priori distribution, the weights ...
will be one for all the neurons in the summation layer. For the input pattern x of an unknown class, a final decision is made through a simple comparison of the PNN outputs, i.e., XCCk, if Ok>°i, i,kC[1,K].
(12)
It can be shown [8] that the output of the PNN is proportional to the aposteriori probability when w()=x=J). This makes the training stage a very straightforward procedure. Although this one-pass non-iterative training process is very fast, a very large network may be formed if the number of samples in the training set is large. However, in our particular application this method is used owing to the limited number of training samples. Also, note that the PNN used by each agent in CMAC is identical, i.e. only one PNN needs to be trained. For a two-class problem, the two outputs of the PNN correspond to class conditional probabilities, i.e., Ok(xi) p(xi Ck), k = 0,1. In order to generate an agent's preliminary decision ui from these two outputs, a simple rule can be used. In this work, the first PNN output, namely 01(xi) (normalized such that 0i(xi) + 62(Xi) = 1) is chosen to represent the preliminary decision, i.e., ui = 6,(xi) = (xi)±2 (x)In this case, ui is interpreted as a confidence measure and can take on values between zero and one. In the a case where ui 1, it is assumed the agent strongly believes a 0, it is assumed that the agent xi Cl, and when ui strongly believes xi e Co. In the case where ui 0.5, it is assumed that the agent is unsure of the class of the given feature vector.
o0
-
D. BPNN Estimation of Class Conditional Probabilities
Once the ith agent's BPNN-based probability estimator has received uir, it estimates the class conditional probabilities p(uj Ck),j 1,...,N; j i such that
yj (k)
p(uj Ck),
(13)
where yj (k) is the kth (k C {0, 1}) element of the BPNN output vector for the input uj. This is done individually for each element in ui,r. Here, it is assumed that p(ui) = p(uj), V i,j C [1,N];i 7 j. This allows us to estimate the a priori class conditional probabilities using the BPNN, which actually produces the a posterior class conditional probabilities yj(k) p(Ck uj). During the training, the goal is to capture the mapping relating the preliminary decisions in the training set to the class conditional probabilities that are used when forming (9). Assuming that a two-layer BPNN with a 1- M -2 structure (where M is the number of hidden layer neurons) is utilized, in most cases the training phase will terminate fairly quickly due to the fact M will normally be quite small. Note that this corresponds to a simple Bayesian classifier [9]. Similar to the PNN, once the BPNN is trained, the same system is used in each agent. Using this definition of the elements of yj(k) given by (13), we can now simplify the final threshold tfi in (9) such -
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that N
P (CO) tf i (Uir)
II yj1(2)
j=l,j7Xi
[J
Joo]
N
P(cl)
yj(i) [Joi
II
-
Jill
j=l,j7Xi
Using the PNN output for the ith agent, A(xi) in (10) becomes
pA(x. (=
Cl(xi)
)
p(xdC(o) 02 (Xi ) The soft final decision ufi for the ith agent is obtained by
A(xi)
Uf,
A (xi) +
tf i(Uir)
(16)
In order to make the CMAC system comparable to other multi-ping classification schemes [4], [5], the set of N final agent decisions are combined to produce a single decision. A fusion rule can be devised, assuming that the local decisions are statistically independent, using a geometric decision averaging given by Yf
N
= 1
Ufi
i=1
1
1,
