多视图Hessian正则化下的半监督稀疏特征选择

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本文主要探讨了"基于多视图海森矩阵正则化的半监督稀疏特征选择"这一主题，由作者Caijuan Shi、Jian Liu、Liping Liu和Xiaodong Yan共同完成，他们来自中国北方工业大学信息工程学院，位于唐山。近年来，随着数据科学的发展，半监督学习在特征选择中的应用日益受到重视，尤其是在处理多视图数据时，传统的单视图方法往往无法充分利用多维度信息。大部分现有的半监督特征选择算法专注于单一视角的数据，而这篇研究旨在克服这一局限。作者注意到，基于拉普拉斯正则化的现有方法在处理半监督问题时缺乏泛化能力，因此提出了一个新颖的框架，即利用多视图海森矩阵正则化来提升特征选择的性能。这种方法旨在通过增强对数据内在结构的理解，更好地挖掘潜在的特征关联和模式。文章的核心贡献是提出了一种简单而高效的迭代优化算法，用于解决目标函数。该算法旨在找到稀疏特征子集，这些子集在多视图数据中既能保持良好的区分性，又能确保模型的解释性和可解释性。作者将这个方法应用到了图像标注任务上，对两个网络图像数据集进行了广泛的实验验证。实验结果显示，与传统方法相比，基于多视图海森矩阵正则化的半监督稀疏特征选择方法能够更有效地筛选出关键特征，从而在图像标注等任务中取得更好的性能。这表明，该方法不仅能在有限的标记数据下提高学习效率，还能扩展到其他半监督学习场景，如文本分类、推荐系统等领域，为多模态数据的特征分析提供了一种有前景的策略。总结来说，这篇文章的主要知识点包括： 1. 半监督稀疏特征选择的重要性及其在多视图数据中的挑战。 2. 多视图海森矩阵正则化的引入，作为对拉普拉斯正则化的改进，增强了特征选择的泛化能力和性能。 3. 提出的迭代优化算法设计及其在实际应用场景（如图像标注）中的有效性。 4. 实验结果的比较和展示，证明了新方法在实际任务中的优越性。通过这篇研究，作者为解决半监督学习中多视图特征选择的问题提供了新的理论和技术支持，对于提高机器学习在复杂数据集上的表现具有重要意义。

Semi-supervised Sparse Feature Selection based on

Multi-view Hessian Regularization

Caijuan Shi, Jian Liu, Liping Liu, Xiaodong Yan

College of Information Engineering, North China University of Science and Technology, Tangshan, China

scj-blue@163.com

Abstract—Semi-supervised sparse feature selection has received

increasing attention in recent years. However, most of the semi-

supervised feature selection algorithms are developed for the

single-view data and cannot naturally handle data represented by

multi-view features. Moreover, most existing semi-supervised

sparse feature selection methods are based on Laplacian

regularization, which is lack of extrapolating power. Therefore,

we present a new semi-supervised sparse feature selection

framework based on multi-view Hessian regularization to obtain

better performance in this paper. A simple yet efficient iterative

method is proposed to solve the objective function. We apply the

proposed method into image annotation task and conduct

extensive experiments on two web image datasets. Experimental

results show that the proposed method can realize feature

selection well.

Keywords-multi-view learning; Hessian regularization; semi-

supervised sparse feature selection; web image annotation.

I. INTRODUCTION

Recently, semi-supervised sparse feature selection

approaches have obtained more and more research interest.

However, most of the existing semi-supervised feature

selection methods, such as [1], [2] and [3], are developed for

single-view data. Once these methods confront with multi-view

data, they often directly concatenate multi-view features into a

long vector. We know each type of feature characterizes these

data in one specific feature space and has particular physical

meaning and statistic property. This concatenation strategy

cannot explore the complementary of different view features

efficiently.

It has shown extensively that multi-view learning can

address the above problem to leverage the correlated and

complemental information between different views. In [4], Xu

et al. have reviewed the multi-view learning in detail. In [5]

Feng et al. have proposed an adaptive unsupervised multi-view

feature selection for visual concept recognition. However, to

the best of our knowledge, multi-view learning has not been

applied into semi-supervised sparse feature selection. In this

paper, we apply multi-view learning into our semi-supervised

sparse feature selection framework to select more compact and

accurate feature.

Though the graph Laplacian based semi-supervised

learning approaches have widely been applied into semi-

supervised feature selection [1] [2], Hessian regularization has

better extrapolating power to boost the semi-supervised

learning performance compared to Laplacian regularization[6].

So we apply Hessian regularization into our multi-view semi-

supervised sparse feature selection framework.

In this paper, we propose a new semi-supervised sparse

feature selection framework based on multi-view Hessian

Regularization, namely Multi-view Hessian Regularization

Feature Selection (MHRFS). MHRFS utilizes multi-view

learning and Hessian regularization simultaneously to boost the

performance of the semi-supervised sparse feature selection.

An effective iterative algorithm is proposed to optimize the

objective function. MHRFS is applied into large-scale web

image annotation task and extensive experiments are conduct

on two web image datasets: NUS-WIDE [7] dataset and

MSRA-MM 2.0 [8] dataset.

II. THE PROPOSED FRAMEWORK

A. MHRFS Formulation

In MHRFS framework, a multi-view training dataset of n

observations from m views is given.

X X X







donated as the training dataset, including q labeled data and n-

q unlabelled data. The feature data matrix of vth view can be

denoted as

 

and the feature data matrix of all views can be

denoted as

     

, , , ,

X X X X R









, where





Given

{0,1}





be the label matrix of training dataset, where

c is the number of classes and

(1 )

y R i n  

is the ith label

vector. Denote

     

, , , ,

F F F F R









as the predicted

label matrix for all views and

()v n c





and the vth view

predicted label matrix respectively. Let





be the

projection matrix, which is regarded as the combination

coefficients for the most discriminative features. In order to

realize sparse feature selection with the optimal projection

matrix G, we exploit the l

2,1/2

-matrix norm as the sparse model

due to its efficacy [1]. Then the sparse feature selection

framework based on l

2,1/2

-matrix norm can be generalized as

the following objective function:

2,1/2

minloss( )





. (1)

where

loss( )G

is the loss function and

2,1/2

is the

regularization term with λ as regularization parameter. The

definition of

2,1/2

is:

ICWMMN2015 Proceedings

177

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