On the consistency of multiclass classification methods

Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that not all generalizations preserve the nice property of Bayes consistency. We provide a necessary and sufficient condition for consistency which applies to a large class of multiclass classification methods. The approach is illustrated by applying it to some multiclass methods proposed in the literature.

Classification with a reject option using a hinge loss

We consider the problem of binary classification where the classifier can, for a particular cost, choose not to classify an observation. Just as in the conventional classification problem, minimization of the sample average of the cost is a difficult optimization problem. As an alternative, we propose the optimization of a certain convex loss function φ, analogous to the hinge loss used in support vector machines (SVMs). Its convexity ensures that the sample average of this surrogate loss can be efficiently minimized. We study its statistical properties. We show that minimizing the expected surrogate loss—the φ-risk—also minimizes the risk. We also study the rate at which the φ-risk approaches its minimum value. We show that fast rates are possible when the conditional probability P(Y=1|X) is unlikely to be close to certain critical values.

On the consistency of multiclass classification methods

Binary classification is a well studied special case of the classification problem. Statistical properties of binary classifiers, such as consistency, have been investigated in a variety of settings. Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that one can lose consistency in generalizing a binary classification method to deal with multiple classes. We study a rich family of multiclass methods and provide a necessary and sufficient condition for their consistency. We illustrate our approach by applying it to some multiclass methods proposed in the literature.

Public sector strategy classification system for shared service identification

The purpose of this conceptual paper is to address the lack of consistent means through which strategies are identified and discussed across theoretical perspectives in the field of business strategy. A standardised referencing system is offered to codify the means by which strategies can be identified, from which new business services and information systems may be derived. This taxonomy was developed using qualitative content analysis study of government agencies’ strategic plans. This taxonomy is useful for identifying strategy formation and determining gaps and opportunities. Managers will benefit from a more transparent strategic design process that reduces ambiguity, aids in identifying and correcting gaps in strategy formulation, and fosters enhanced strategic analysis. Key benefits to academics are the improved dialogue in strategic management field and suggest that progress in the field requires that fundamentals of strategy formulation and classification be considered more carefully. Finally, the formalization of strategy can lead to the clear identification of new business services, which inform ICT investment decisions and shared service prioritisation.

Exponentiated gradient algorithms for large-margin structured classification

We consider the problem of structured classification, where the task is to predict a label y from an input x, and y has meaningful internal structure. Our framework includes supervised training of Markov random fields and weighted context-free grammars as special cases. We describe an algorithm that solves the large-margin optimization problem defined in [12], using an exponential-family (Gibbs distribution) representation of structured objects. The algorithm is efficient—even in cases where the number of labels y is exponential in size—provided that certain expectations under Gibbs distributions can be calculated efficiently. The method for structured labels relies on a more general result, specifically the application of exponentiated gradient updates [7, 8] to quadratic programs.

Identification of area-level influences on regions of high cancer incidence in Queensland, Australia : a classification tree approach

Background: Strategies for cancer reduction and management are targeted at both individual and area levels. Area-level strategies require careful understanding of geographic differences in cancer incidence, in particular the association with factors such as socioeconomic status, ethnicity and accessibility. This study aimed to identify the complex interplay of area-level factors associated with high area-specific incidence of Australian priority cancers using a classification and regression tree (CART) approach. Methods: Area-specific smoothed standardised incidence ratios were estimated for priority-area cancers across 478 statistical local areas in Queensland, Australia (1998-2007, n=186,075). For those cancers with significant spatial variation, CART models were used to identify whether area-level accessibility, socioeconomic status and ethnicity were associated with high area-specific incidence. Results: The accessibility of a person’s residence had the most consistent association with the risk of cancer diagnosis across the specific cancers. Many cancers were likely to have high incidence in more urban areas, although male lung cancer and cervical cancer tended to have high incidence in more remote areas. The impact of socioeconomic status and ethnicity on these associations differed by type of cancer. Conclusions: These results highlight the complex interactions between accessibility, socioeconomic status and ethnicity in determining cancer incidence risk.

Glycosaminoglycan and growth factor mediated murine calvarial cell proliferation

Understanding the complex mechanisms underlying bone remodeling is crucial to the development of novel therapeutics. Glycosaminoglycans (GAGs) localised to the extracellular matrix (ECM) of bone are thought to play a key role in mediating aspects of bone development. The influence of isolated GAGs was studied by utilising in vitro murine calvarial monolayer and organ culture model systems. Addition of GAG preparations extracted from the cell surface of human osteoblasts at high concentrations (5 microg/ml) resulted in decreased proliferation of cells and decreased suture width and number of bone lining cells in calvarial sections. When we investigated potential interactions between the growth factors fibroblast growth factor-2 (FGF2), bone morphogenic protein-2 (BMP2) and transforming growth factor-beta1 (TGFbeta1) and the isolated cell surface GAGs, differences between the two model systems emerged. The cell culture system demonstrated a potentiating role for the isolated GAGs in the inhibition of FGF2 and TGFbeta1 actions. In contrast, the organ culture system demonstrated an enhanced stimulation of TFGbeta1 effects. These results emphasise the role of the ECM in mediating the interactions between GAGs and growth factors during bone development and suggest the GAG preparations contain potent inhibitory or stimulatory components able to mediate growth factor activity.