SLEM：基于稀疏标签编码的多维分类新方法

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"这篇论文是ICML2021上发表的，名为‘基于稀疏标签编码的多维分类’，作者是Bin-Bin Jia和Min-Ling Zhang。研究主要集中在多维分类（MDC）问题上，该问题涉及多个类变量，每个变量对应一个异构类空间。传统方法在处理这类问题时面临的挑战在于如何处理不同类变量间的依赖关系。" 正文: 在多维分类任务中，输出空间通常包含多个类变量，这些变量可能属于不同的类别结构，这使得建模和预测变得复杂。传统的分类方法在处理这样的异构数据时可能会遇到困难，因为它们难以捕捉类变量之间的相互作用。这篇论文介绍了一种名为SLEM（Sparse Label Encoding）的新方法，它创新性地将预测模型的学习从原始的异构标签空间转移到经过编码的标签空间。 SLEM的核心是一个编码-训练-解码框架。首先，在编码阶段，SLEM运用三个连续的操作来转换类向量：1) 对对分组，这有助于发现和处理类变量之间的关联；2) 一次热转换，将离散的类标签转化为连续的表示，便于后续处理；3) 稀疏线性编码，进一步压缩并减少冗余，使编码后的向量更加简洁。接下来，在训练阶段，SLEM在经过编码的标签空间中学习一个多输出回归模型。相比于传统的分类模型，多输出回归模型可以更好地处理连续的、编码后的标签，同时考虑到所有类变量的整体效应。最后，解码阶段使用正交匹配追踪(Orthogonal Matching Pursuit, OMP)算法来从学习到的多输出回归模型的输出中恢复预测的类向量。OMP是一种有效的稀疏信号恢复技术，它能从编码后的连续向量中找到与原始类向量最匹配的解。实验结果显示，SLEM在处理多维分类问题时，相较于现有的先进方法，表现出显著的优越性能。这表明，通过SLEM的编码策略，能够更有效地捕获和利用类变量之间的依赖信息，从而提高多维分类的准确性和效率。 SLEM提供了一个强大的工具来解决多维分类问题，特别是当类空间具有异质性时。它通过编码标签空间，使得建模和学习过程更加高效，并且通过实验验证了这种方法的有效性。这种创新的方法对于推动多维分类领域的研究和技术发展具有重要意义。

Multi-Dimensional Classiﬁcation via Sparse Label Encoding

Bin-Bin Jia

1 2

Min-Ling Zhang

1 3

Abstract

In multi-dimensional classiﬁcation (MDC), there

are multiple class variables in the output space

with each of them corresponding to one hetero-

geneous class space. Due to the heterogeneity

of class spaces, it is quite challenging to consid-

er the dependencies among class variables when

learning from MDC examples. In this paper, we

propose a novel MDC approach named SLEM

which learns the predictive model in an encoded

label space instead of the original heterogeneous

one. Speciﬁcally, SLEM works in an encoding-

training-decoding framework. In the encoding

phase, each class vector is mapped into a real-

valued one via three cascaded operations includ-

ing pairwise grouping, one-hot conversion and

sparse linear encoding. In the training phase, a

multi-output regression model is learned within

the encoded label space. In the decoding phase,

the predicted class vector is obtained by adapting

orthogonal matching pursuit over outputs of the

learned multi-output regression model. Experi-

mental results clearly validate the superiority of

SLEM against state-of-the-art MDC approaches.

1. Introduction

In traditional supervised learning, the semantics of objects

are usually characterized by only one output variable, e.g.,

multi-class classiﬁcation. However, in some real-world ap-

plications, the semantics of objects need to be characterized

along different dimensions. For example, the e-commerce

websites should categorize laptops from different dimen-

sions (e.g., brand, operating system, CPU, GPU, etc.) to

make it more convenient for consumers to choose the right

laptop for themselves. In fact, similar requirements widely

School of Computer Science and Engineering, Southeast Uni-

versity, Nanjing 210096, China

College of Electrical and Infor-

mation Engineering, Lanzhou University of Technology, Lanzhou

730050, China

Key Lab. of Computer Network and Information

Integration (Southeast University), Ministry of Education, China.

Correspondence to: Min-Ling Zhang <zhangml@seu.edu.cn>.

Proceedings of the

International Conference on Machine

exist in various ﬁelds, e.g., text classiﬁcation (Shatkay et al.,

2008), bioinformatics (Rodr

ıguez et al., 2012), resource al-

location (Al Muktadir et al., 2019), ecology (Verma et al.,

2021), etc. These special applications can be naturally for-

malized under the multi-dimensional classiﬁcation (MDC)

learning framework (Read et al., 2014a; Ma & Chen, 2018;

Jia & Zhang, 2020a; Wang et al., 2020). In MDC, each

example is represented by a single instance while associat-

ed with multiple class variables. Here, each class variable

corresponds to one speciﬁc class space which characterizes

the semantics of objects from one dimension.

Formally speaking, let

X = R

be the input (feature) s-

pace, and

Y = C

× C

× ··· × C

be the output space

which corresponds to the Cartesian product of

class s-

paces. Here, each class space

(1 ≤ j ≤ q)

consists

possible class labels, i.e.,

= {c

, c

, . . . , c

}

Given the MDC training set

D = {(x

, y

) | 1 ≤ i ≤ m}

with

training examples, for each example

, y

) ∈ D

= [x

, x

, . . . , x

]

∈ X

is a

-dimensional feature

vector and y

= [y

, y

, . . . , y

]

∈ Y is the class vector

associated with

, where each component

is one possi-

ble item in

, i.e.,

∈ C

. The MDC task aims to learn

a predictive model

f : X 7→ Y

from

which can return a

proper class vector f(x) ∈ Y for unseen instance x.

To solve the MDC problem, we can independently deal with

each dimension which is actually a multi-class classiﬁca-

tion problem. Nonetheless, this strategy does not consider

potential dependencies among class spaces which would de-

generate its generalization ability. Therefore, most existing

MDC studies focus on how to model class dependencies

more appropriately, e.g., specifying a chaining structure over

class variables (Zaragoza et al., 2011; Read et al., 2014b),

partitioning class spaces into several groups (Read et al.,

2014a), learning a direct acyclic graph structure over class

variables (Bielza et al., 2011; Gil-Begue et al., 2021), etc.

Due to the heterogeneity of class spaces, it is quite chal-

lenging to directly consider the dependencies among class

variables in the original output space as most existing MDC

approaches do. In this paper, we attempt to learn the pre-

dictive model which solves the MDC problem in its trans-

formed label space. Accordingly, we propose a novel ap-

proach named SLEM, i.e., Sparse Label Encoding for Multi-

dimensional classiﬁcation, which works in an encoding-

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