Multiple Class Variables Research Articles

Introducing multi-dimensional hierarchical classification: Characterization, solving strategies and performance measures

Classification problems where there exist multiple class variables that need to be jointly predicted are known as Multi-dimensional classification problems. If the labels of these class variables are organized as hierarchies, we can take advantage of specific strategies designed for the Hierarchical classification paradigm. In this paper we present the Multi-dimensional hierarchical classification (MDHC) paradigm, a result of the combination of Multi-dimensional and Hierarchical classification paradigms. We propose four MDHC learning strategies which are designed to exploit the particularities of this new paradigm, combining characteristics of Multi-dimensional and Hierarchical classification strategies. Along with these strategies, we present a framework for classifier comparison in which we use a set of performance measures specifically designed for MDHC, and a procedure to create MDHC synthetic scenarios. Using this framework and the performance measures presented, we study how characteristics of the MDHC problems influence the performance of the different MDHC strategies proposed, and compare them to other non-MDHC strategies.

Decomposition-Based Classifier Chains for Multi-Dimensional Classification

In multi-dimensional classification, the semantics of objects are characterized by multiple class variables from different dimensions. To model the dependencies among class variables, one natural strategy is to build a number of multiclass classifiers in a chaining structure, one per dimension, where the subsequent classifiers on the chain augment the feature space with all labeling information used by the preceding classifiers. However, it is shown that this strategy cannot compete with existing state-of-the-art approaches via comparative studies. One possible reason is that inaccurate predictions of preceding classifiers would degenerate the performance of subsequent ones. Besides, it is more difficult to learn a multiclass classifier than a binary one with the same accuracy, and better performance can be expected if the multi-dimensional classification problem can be solved by building multiple binary classifiers in a chaining structure. Based on these conjectures, this article proposes an approach, which builds a chain of binary classifiers to solve the multi-dimensional classification problem with the help of one-versus-one decomposition. To address the issue that different one-versus-one decomposed problems involve different training examples, the feature space is augmented with the binary predictions of preceding classifiers on the chain to train the subsequent ones. To alleviate the effect of the specified chaining order, the ensemble version of the proposed approach is further investigated. Comparative studies over 20 benchmark datasets clearly show the superiority of the proposed approach against the state-of-the-art multi-dimensional classification baselines.

Multidimensional continuous time Bayesian network classifiers

The multidimensional classification of multivariate time series deals with the assignment of multiple classes to time-ordered data described by a set of feature variables. Although this challenging task has received almost no attention in the literature, it is present in a wide variety of domains, such as medicine, finance or industry. The complexity of this problem lies in two nontrivial tasks, the learning with multivariate time series in continuous time and the simultaneous classification of multiple class variables that may show dependencies between them. These can be addressed with different strategies, but most of them may involve a difficult preprocessing of the data, high space and classification complexity or ignoring useful interclass dependencies. Additionally, no attention has been given to the development of new multidimensional classifiers of time series based on probabilistic graphical models, even though transparent models can facilitate further understanding of the domain. In this paper, a novel probabilistic graphical model is proposed, which is able to classify a discrete multivariate temporal sequence into multiple class variables while modeling their dependencies. This model extends continuous time Bayesian networks to the multidimensional classification problem, which are able to explicitly represent the behavior of time series that evolve over continuous time. Different methods for the learning of the parameters and structure of the model are presented, and numerical experiments on synthetic and real-world data show encouraging results in terms of performance and learning time with respect to independent classifiers, the current alternative approach under the continuous time Bayesian network paradigm.

Multi-dimensional Bayesian network classifiers: A survey

Multi-dimensional classification is a cutting-edge problem, in which the values of multiple class variables have to be simultaneously assigned to a given example. It is an extension of the well known multi-label subproblem, in which the class variables are all binary. In this article, we review and expand the set of performance evaluation measures suitable for assessing multi-dimensional classifiers. We focus on multi-dimensional Bayesian network classifiers, which directly cope with multi-dimensional classification and consider dependencies among class variables. A comprehensive survey of this state-of-the-art classification model is offered by covering aspects related to their learning and inference process complexities. We also describe algorithms for structural learning, provide real-world applications where they have been used, and compile a collection of related software.

Multi-dimensional classification via kNN feature augmentation

In multi-dimensional classification (MDC), each training example is represented by a single instance (feature vector) while associated with multiple class variables, each of which specifies its class membership w.r.t. one specific class space. Most existing MDC approaches try to model dependencies among class variables in output space when inducing predictive functions, while the potential usefulness of manipulating feature space hasn’t been investigated. As a first attempt towards feature manipulation in input space for MDC, a simple yet effective approach named Kram is proposed which enriches the original feature space with augmented features based on kNN techniques. Specifically, simple counting statistics on the class membership of neighboring MDC examples as well as distance information between MDC examples and their k nearest neighbors are used to generate augmented feature vector. In this way, discriminative information from class space is expected to be brought into the feature space which would be helpful to the following MDC predictive model induction. To validate the effectiveness of the proposed feature augmentation techniques, comprehensive comparative studies are conducted over fifteen benchmark data sets. Compared to the original feature space, it is clearly shown that the kNN-augmented features generated by the proposed Kram approach can significantly improve generalization abilities of existing MDC approaches.

Multi-Dimensional Classification via kNN Feature Augmentation

Multi-dimensional classification (MDC) deals with the problem where one instance is associated with multiple class variables, each of which specifies its class membership w.r.t. one specific class space. Existing approaches learn from MDC examples by focusing on modeling dependencies among class variables, while the potential usefulness of manipulating feature space hasn’t been investigated. In this paper, a first attempt towards feature manipulation for MDC is proposed which enriches the original feature space with kNNaugmented features. Specifically, simple counting statistics on the class membership of neighboring MDC examples are used to generate augmented feature vector. In this way, discriminative information from class space is encoded into the feature space to help train the multi-dimensional classification model. To validate the effectiveness of the proposed feature augmentation techniques, extensive experiments over eleven benchmark data sets as well as four state-of-the-art MDC approaches are conducted. Experimental results clearly show that, compared to the original feature space, classification performance of existing MDC approaches can be significantly improved by incorporating kNN-augmented features.

Multi-Dimensional Classification with Super-Classes

The multi-dimensional classification problem is a generalization of the recently-popularized task of multi-label classification, where each data instance is associated with multiple class variables. There has been relatively little research carried out specific to multi-dimensional classification and, although one of the core goals is similar (modeling dependencies among classes), there are important differences; namely a higher number of possible classifications. In this paper we present method for multi-dimensional classification, drawing from the most relevant multi-label research, and combining it with important novel developments. Using a fast method to model the conditional dependence between class variables, we form super-class partitions and use them to build multi-dimensional learners, learning each super-class as an ordinary class, and thus explicitly modeling class dependencies. Additionally, we present a mechanism to deal with the many class values inherent to super-classes, and thus make learning efficient. To investigate the effectiveness of this approach we carry out an empirical evaluation on a range of multi-dimensional datasets, under different evaluation metrics, and in comparison with high-performing existing multi-dimensional approaches from the literature. Analysis of results shows that our approach offers important performance gains over competing methods, while also exhibiting tractable running time.

Supervised pre-processing approaches in multiple class variables classification for fish recruitment forecasting

A multi-species approach to fisheries management requires taking into account the interactions between species in order to improve recruitment forecasting of the fish species. Recent advances in Bayesian networks direct the learning of models with several interrelated variables to be forecasted simultaneously. These models are known as multi-dimensional Bayesian network classifiers (MDBNs). Pre-processing steps are critical for the posterior learning of the model in these kinds of domains. Therefore, in the present study, a set of ‘state-of-the-art’ uni-dimensional pre-processing methods, within the categories of missing data imputation, feature discretization and feature subset selection, are adapted to be used with MDBNs. A framework that includes the proposed multi-dimensional supervised pre-processing methods, coupled with a MDBN classifier, is tested with synthetic datasets and the real domain of fish recruitment forecasting. The correctly forecasting of three fish species (anchovy, sardine and hake) simultaneously is doubled (from 17.3% to 29.5%) using the multi-dimensional approach in comparison to mono-species models. The probability assessments also show high improvement reducing the average error (estimated by means of Brier score) from 0.35 to 0.27. Finally, these differences are superior to the forecasting of species by pairs.

Art in Bourgeois Society: 1790-1850

Art in Bourgeois Society: 1790-1850 Hemingway, A., & Vaughan, W. (Eds.). (1998). Cambridge: University Press. 372 pages. (ISBN:0521-55182-X) Reviewed by Kin-Keifer-Boyd, Texas Tech University Most would concur that class division and struggle affect our sense of self and conception of historical development, but what exactly is that effect? How do we participate in the creation of class distinctions? Whose struggle will ignite future historical shifts? What directions are possible? According to Marxism, class struggle is the motor of historical change (Hemingway, 1998, p. 10). Art in Bourgeois Society is an analytical gem for those interested in an historical perspective on such issues. The scholarship is thorough and the writing straightforward. In the book's introduction, Hemingway (1998) argues that societies were only a parody of socialism, and Soviet Marxism but a travesty of Marxist (p. 1) and demonstrates how neo-Marxist critique has redefined Marxism after the fall of Communism. Marxism is a social theory aimed at elucidating causal structures for social change. While classical Marxism, derived from the writings of Marx and Engels, concerned the essential nature of class relations, this text presents contemporary or analytical Marxism, and posits that multiple class variables (i.e., economic capital, educational capital, social capital, and cultural capital) all affect each other. From an analytical Marxist perspective, one might investigate-as the authors of this book do-how art activities are constrained or shaped by economic, institutional, and educational capital. The book involves contemporary Marxist analyses of art patronage, art representing class identity, and art a signifier of national identity. It explores how art embodied institutionalized notions of nature and society within the Modernist epoch of 1790-1850 in Britain (chapters 1-5), France (chapters 6-8), Germany (chapters 9-12) and the United States (chapters 13-15). While there is diversity within contemporary Marxist theory, the common bond in these 15 chapters is that the analyses are anti-positivist, multi-causal, and eschew any simple progressivism (p. 3). Researchers who inquire into different exploitative relationships between artists, curators, collectors, art critics, and historians will find the book helpful in developing methodology framed in Marxist theory. The 10-page index is useful for locating theorists, artists, artworks, concepts and interpretative strategies discussed within the book for those engaged in such research. Highlights of the four sections follow. Hemingway provides historical and contextual information in his introductions to the four sections. In the introduction to section one on Britain, he reminds us that Britain and France engaged in nearly 20 years of continuous warfare between 1793 and 1815 (p. 22). British bourgeois feminized the popular notion of France, thus degrading the country's art overly passionate and flaunting narcissism. Ann Pullan's discussion, in chapter one, of the foundation of Britain's National Gallery in 1824 makes it clear that those who owned property decided the cultural collections of the nation. Their property, of course, is what they deemed most valuable. This is an enduring pattern. When Sir Charles Angerstein's collection of 38 paintings was purchased for the nation, his family blood-lineage became the Trustees of the British Gallery (p. 29). At first the public purchase was housed in a private residence. The Trustees (i.e., Angerstein's heirs) promised those who bought engraved reproductions of the paintings that they could view the works, a strategy to collect membership dues through subscriptions. The British National Gallery at this time resembled rooms of a private mansion, complete with crimson wall paper and velvet hangings with twice-yearly exhibitions chosen by the Trustees [consisting of bankers and aristocracy] functioning as visible and symbolic reminders of patrician and royal authority (p. …