A Novel Border Identification Algorithm Based on an “Anti-Bayesian” Paradigm

2020

Pattern Anal Applic

Self Cite

Parametric and nonparametric pattern recognition have been studied for almost a century based on a Bayesian paradigm, which is, in turn, founded on the principles of Bayes theorem. It is well-known that the accuracy of the Bayes classifier cannot be exceeded. Typically, this reduces to comparing the testing sample to mean or median of the respective distributions. Recently, Oommen and his co-authors have presented a pioneering and nonintuitive paradigm, namely, that of achieving the classification by comparing the testing sample with another descriptor, which could also be quite distant from the mean. This paradigm has been termed as being "Anti-Bayesian", and it essentially uses the quantiles of the distributions to achieve the pattern recognition. Such classifiers attain the optimal Bayesian accuracy for symmetric distributions even though they operate with a non-intuitive philosophy. While this paradigm has been applied in a number of domains (briefly explained in the body of this paper), its application for nonparametric domains has been limited. This paper explains, in detail, how such quantile-based classification can be extended to the nonparametric world, both using traditional and kernel-based strategies. The paper analyzes the methodology of such nonparametric schemes and their robustness. From a fundamental perspective, the paper utilizes the so-called "Large Sample" theory to derive strong asymptotic results that pertain to the equivalence between the parametric and nonparametric schemes for large samples. Apart from the new theoretical results, the paper also presents experimental results demonstrating their power. These re-

Section: Q11mentioning

confidence: 99%

Section: Nonparametric Classification Based On Empirical Quantilesmentioning

confidence: 99%

See 1 more Smart Citation

Nonparametric “anti-Bayesian” quantile-based pattern classification

Mahmoudi

Razmkhah

2020

Pattern Anal Applic

Self Cite

“…In [30], the authors further proposed a new border identication algorithm, namely the AB Border Identication scheme. For each class, this method selects, as the corresponding border points, a small number of data points that lie close to the discriminant function's boundary, but where these points are not within the central part of the class conditional distributions.…”

Section: Related Work On Antibayesian Prmentioning

confidence: 99%

On the classification of dynamical data streams using novel “Anti-Bayesian” techniques

Hammer

Yazidi

2018

Pattern Recognition

Self Cite

The classication of dynamical data streams is among the most complex problems encountered in classication. This is, rstly, because the distribution of the data streams is nonstationary, and it changes without any prior warning. Secondly, the manner in which it changes is also unknown. Thirdly, and more interestingly, the model operates with the assumption that the correct classes of previously-classied patterns become available at a juncture after their appearance. This paper pioneers the use of unreported novel schemes that can classify such dynamical data streams by invoking the recently-introduced Anti-Bayesian (AB) techniques.Contrary to the Bayesian paradigm, that compare the testing sample with the distribution's central points, AB techniques are based on the information in the distant-from-the-mean samples.Most Bayesian approaches can be naturally extended to dynamical systems by dynamically tracking the mean of each class using, for example, the exponential moving average based estimator, or a sliding window estimator. The AB schemes introduced by Oommen et al., on the other hand, work with a radically dierent approach and with the non-central quantiles of the distributions. Surprisingly and counter-intuitively, the reported AB methods work equally or close-to-equally well to an optimal supervised Bayesian scheme on a host of accepted Pattern Recognition problems. This thus begs its natural extension to the unexplored arena of classication for dynamical data streams. Naturally, for such an AB classication approach, we need to track the non-stationarity of the quantiles of the classes. To achieve this, in this paper, we develop an AB approach for the online classication of data streams by applying the ecient and robust quantile estimators developed by Yazidi and Hammer [12,37].

“…In [9], the authors further proposed a new border identification algorithm, namely the AB Border Identification scheme. For each class, this method selects, as the corresponding border points, a small number of data points that lie close to the discriminant function's boundary, but where these points are not within the central part of the class conditional distributions.…”

Section: A Related Work On "Anti-bayesian" Prmentioning

confidence: 99%

On using novel “Anti-Bayesian” techniques for the classification of dynamical data streams

Hammer

Yazidi

2017 IEEE Congress on Evolutionary Computation (CEC)

2017

Self Cite

The classification of dynamical data streams is among the most complex problems encountered in classification. This is, firstly, because the distribution of the data streams is non-stationary, and it changes without any prior "warning". Secondly, the manner in which it changes is also unknown. Thirdly, and more interestingly, the model operates with the assumption that the correct classes of previously-classified patterns become available at a juncture after their appearance. This paper pioneers the use of unreported novel schemes that can classify such dynamical data streams by invoking the recentlyintroduced "Anti-Bayesian" (AB) techniques. Contrary to the Bayesian paradigm, that compare the testing sample with the distribution's central points, AB techniques are based on the information in the distant-from-the-mean samples.Most Bayesian approaches can be naturally extended to dynamical systems by dynamically tracking the mean of each class using, for example, the exponential moving average based estimator, or a sliding window estimator. The AB schemes introduced by Oommen et al., on the other hand, work with a radically different approach and with the non-central quantiles of the distributions. Surprisingly and counter-intuitively, the reported AB methods work equally or close-to-equally well to an optimal supervised Bayesian scheme on a host of accepted PR problems. This thus begs its natural extension to the unexplored arena of classification for dynamical data streams. Naturally, for such an AB classification approach, we need to track the non-stationarity of the quantiles of the classes. To achieve this, in this paper, we develop an AB approach for the online classification of data streams by applying the efficient and robust quantile estimators developed by Yazidi and Hammer [3], [13].Apart from the methodology itself, in this paper, we compare the Bayesian and AB approaches. The results demonstrate the intriguing and counter-intuitive results that the AB approach shows competitive results to the Bayesian approach. Furthermore, the AB approach is much more robust against outliers, which is an inherent property of quantile estimators [3], [13], which is a property that the