Three-way decisions based blocking reduction models in hierarchical classification

Highlights

• Two three-way decisions based hierarchical classification models are proposed.

• The ambiguity of hierarchy is noticed and 3WD is used to reduce the uncertainty.

• The topic model is used to learn category relations.

• The proposed models perform better than several hierarchical classification methods.

• Extend the application domain of three-way decisions to fashion image classification.

Abstract

Hierarchical classification (HC) is effective when categories are organized hierarchically. However, the blocking problem makes the effect of hierarchical classification greatly reduced. Blocking means that samples are easily getting misclassified in high-level classifiers so that the samples are blocked at the high-level of the hierarchy. This issue is caused by the inconsistency between the artificially defined hierarchy and the actual hierarchy of the raw data. Another issue is that it is flippant to strictly process data following the hierarchy. Therefore, special treatment is required for some uncertain data. To address the first issue, we learn category relationships and modify the hierarchy. To address the second issue, we introduce three-way decisions (3WD) to targetedly deal with the ambiguous data. We extend original studies and propose two HC models based on 3WD, collectively referred to as TriHC, for carefully modifying the hierarchy to alleviate the blocking problem. The proposed TriHC model learns new category hierarchies by the following three steps: (1) mining category relations; (2) modifying category hierarchies according to the latent category relations; and (3) using 3WD to divide observed objects into three regions: positive region, boundary region, and negative region, and making decisions based on different strategies. Specifically, based on different category relation mining methods, there are two versions of TriHC, cross-level blocking priori knowledge based TriHC (CLPK-TriHC) and expert classifier based TriHC (EC-TriHC). The CLPK-TriHC model defines a cross-level blocking distribution matrix to mine the category relations between the higher and lower levels. To better exploit category hierarchical relations, the EC-TriHC model builds expert classifiers using topic model to learn latent category topics. Experimental results validate that the proposed methods can simultaneously reduce the blocking and improve the classification accuracy.

Introduction

Hierarchical classification (HC) is an effective method to solve multiclass classification problems, especially when categories are organized hierarchically. Many important real-world classification problems naturally can be treated as HC problems, such as text categorization [4], [14], protein function prediction [27], [33], image classification [2], [6] etc. Using HC methods, a large-scale classification task can be divided into several small-scale tasks, so as to reduce the difficulty of classification. Usually, HC method uses a top-down level-based strategy, in which the class hierarchy typically stored as a tree. Such a strategy is simple, intuitive, and interpretable. However, due to the complexity of category relationships, samples are easily misclassified in higher-level classifiers, i.e. blocking. It is clear that blocking is one of reasons that HC performs worse than the traditional flat classification.

Most existing blocking reduction strategies in HC can be divided into two types depending on whether changing the category hierarchy: methods that will change the hierarchy and methods that will not change the hierarchy. For the first type, there are Restricted Voting method (RVM) [37], Priori Knowledge Based Hierarchical Classification method (PKHC) [40], data-driven hierarchical structure modification approach (Global-INF) [25], and etc. These strategies give the blocked samples another chance to return to the correct categories by changing the original hierarchy. For the second type, there are Multiplicative method (MM) [7], Extended Multiplicative method (EMM) [37], Threshold Reduction Method (TRM) [37], and etc. These strategies work on probabilities of base classifiers, taking into account the horizontal or vertical base classifiers’ results and helping blocked samples return to the correct category. In fact, methods of the second type have little improvement in the blocking problem. Since blocking is mainly caused by the complexity of category relationships, methods which change the hierarchy are more suitable for the blocking reduction problems. The two blocking reduction strategies proposed in this paper also belong to the first type.

Although there are many methods of the first type have been presented in the past, less of them considers the inconsistency between the artificially defined hierarchy and the actual hierarchy of the data. Some of existing methods take into account the relationship between base classifiers, but overrefine the hierarchical topological structure, which bring new blocking. Take PKHC method as an example, let us consider the most extreme case, high-level category H₁ has two sub-categories L₁₁ and L₁₂, and all samples of L₁₁ are misclassified as H₂ at the high-level of the hierarchy, while all samples of L₁₂ are classified correcetly as H₁, see Fig. 2. PKHC thinks that samples of H₁ are easily to be misclassified as H₂, thus it will add both paths from H₂ to L₁₁ and L₁₂, it increases training costs and increases the uncertainty of classifier ${\sigma }_{H_2}$. Actually, only the path from H₂ to L₁₁ need to be added. See Section 3 for more details.

To this end, in this study, we propose a new method for blocking reduction problems, the illustration of this method see Fig. 1. In a nutshell, the core of our method is to reconstruct the topology of the hierarchical classification model by learning category relations from the original category hierarchy, then using 3WD method to divide observed objects into three regions: positive region, boundary region and negative region, specially paying attention to the boundary region. We utilize two different methods to mine category relations. The first method takes into account the cross-level blocking priori knowledge based on the method proposed in paper [40], which only considers the relationships between high-level categories but neglects the relationships between high- and low-level categories. However, this method cares only the one-to-one relationships between categories, the second method applies the topic model based label grouping algorithm proposed in paper [39] to learn the many-to-many relationships amongst categories.

The proposed TriHC method can effectively reduce the blocking error and has less impact on categories that are not prone to blocking. Contributions of this study could be summarized as follows.

• We propose two hierarchical models to modify the category hierarchy to deal with blocking problems caused by the inconsistency between the artificially defined hierarchy and the actual hierarchy of the data.

• We explore three-way decisions to alleviate the classification errors caused by data uncertainty.

Our experiments on the challenging DeepFashion dataset [23] and Stanford Dogs dataset [13] demonstrate the effectiveness of the proposed models. We validate that our TriHC models can significantly reduce the blocking problem when compared with several previous HC models. The classification accuracy can even be higher than that of the well trained deep convolutional neural network model.