Delta Divergence: A Novel Decision Cognizant Measure of Classifier Incongruence

Abstract

In pattern recognition, disagreement between two classifiers regarding the predicted class membership of an observation can be indicative of an anomaly and its nuance. Since, in general, classifiers base their decisions on class a posteriori probabilities, the most natural approach to detecting classifier incongruence is to use divergence. However, existing divergences are not particularly suitable to gauge classifier incongruence. In this paper, we postulate the properties that a divergence measure should satisfy and propose a novel divergence measure, referred to as delta divergence. In contrast to existing measures, it focuses on the dominant (most probable) hypotheses and, thus, reduces the effect of the probability mass distributed over the non dominant hypotheses (clutter). The proposed measure satisfies other important properties, such as symmetry, and independence of classifier confidence. The relationship of the proposed divergence to some baseline measures, and its superiority, is shown experimentally.

An Incongruence-Based Anomaly Detection Strategy for Analyzing Water Pollution in Images from Remote Sensing

“…Kittler et al in [13] proposed a taxonomy of anomalies which expanded the concept of anomaly beyond the conventional meaning of outlier. They used sensory data quality assessment [26], contextual [9] and non-contextual [27][28][29][30] classifiers [5,[15][16][17][18], and an incongruence indicator [16][17][18] to identify each type of anomaly [13]. According to this taxonomy [13] anomalies can be, for example, of the types unknown object, measurement model drift, unknown structure, unexpected structural component, component model drift, and unexpected structure and structural components.…”

“…This taxonomy [13] is well-known and widely accepted by the scientific community because it has the potential to be applied for solving problems in many different research areas [13]. Therefore, studies related to the application of the taxonomy [13] on synthetic data are common, such as in [16][17][18]. However, to the knowledge of the authors, studies have not addressed the practical application of the taxonomy [13] to solve real-world problems [2,[31][32][33], because it remains a challenge for all research areas.Anomaly detection [13] and incongruence [15][16][17][18] are two powerful computational tools from pattern recognition (PR) [3,[11][12][13][14][15][16][17][18]34,35] and computer vision (CV) [3,36].…”

“…In this case, for example, a decision-making system should itself first identify a problem with the minimum interaction with humans before offering an adequate solution that could be based on spectral analysis [61]. A decision-making system [13,[16][17][18] is a software installed in a computer which needs to identify different types of problems in order to automatically select appropriate responses to deal with each type of problem [13]. In other words, the machine should choose the appropriate response to the detected problem based on the type of anomaly identified by the system that could be, for example, unexpected structure and structural components [13].…”

“…In this research, the real-world situation captured in images from remote sensing which inspired us to investigate solutions in PR and CV is water pollution, mainly regarding occurrences of disasters [31][32][33]. If this situation could be revealed by the disagreement between classifiers [13,[15][16][17][18], then water pollution could be discovered by anomaly detection [13].Therefore, this paper presents an incongruence-based anomaly detection strategy for analyzing images from remote sensing, with the aim of describing its practical application in detecting water pollution. Therefore, the practical application of the taxonomy [13] is introduced as a strategy for detecting anomalies in real-world application [31-33], i.e., non-synthetic data present in images from remote sensing.…”

“…Therefore, the practical application of the taxonomy [13] is introduced as a strategy for detecting anomalies in real-world application [31-33], i.e., non-synthetic data present in images from remote sensing. We used divergence [16,17] between two image classifications [5,13,[15][16][17][18] (contextual [9] and non-contextual [8,[27][28][29][30]) in order to detect incongruence [13,[15][16][17][18], revealing the presence of anomalies [13]. This research focuses only on the detection of anomalies of the type unexpected structure and structural components, which have been described by Kittler et al in [13].This paper is organized as follows: Section 2 presents a background; Section 3 comments on related work; Section 4 summarizes the proposed strategy; Section 5 describes the materials and methods used for performing the experiments; Section 6 reviews the achieved results; Section 7 discusses the results and Section 8 presents the conclusions.…”