自适应半监督降维方法：ASSDR探索

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"自适应半监督降维方法的研究与应用" 在当前大数据时代，高维数据的积累速度日益加快，这使得维度降低在实际数据处理和分析任务中变得越来越重要。半监督学习是一种介于无监督学习和有监督学习之间的方法，尤其在标注数据有限的情况下，能有效利用未标记数据提升模型的性能。本文聚焦于基于成对约束的半监督降维技术，这些约束可以是同一类别的实例对（must-link约束）或不同类别的实例对（cannot-link约束），以此来提供领域知识。本文提出了一种新颖的半监督降维方法，名为Adaptive Semi-Supervised Dimensionality Reduction（ASSDR）。ASSDR的主要创新点在于它能够自适应地调整成对约束的权重，以优化原始数据的低维表示。这种方法考虑了两类约束条件，通过在降维过程中同时考虑它们，能够更好地保留数据的结构信息和类别信息。在ASSDR中，首先，利用有标签数据构建分类模型，然后将未标记数据映射到该模型的决策边界附近。接着，根据成对约束调整实例在低维空间中的位置，使得满足must-link约束的实例尽可能接近，而满足cannot-link约束的实例尽可能远离。这个过程通过迭代优化进行，每次迭代中，ASSDR会更新权重以更准确地反映实例间的相似性和类别关系。为了评估ASSDR的有效性，论文进行了大量的实验，对比了其他几种流行的半监督降维方法，如LLE（局部线性嵌入）、ISOMAP（等距映射）和SSLLE（半监督局部线性嵌入）。实验结果表明，ASSDR在多种数据集上都能取得优秀的分类性能和降维效果，特别是在处理大规模、高维度数据时，其优势更为明显。此外，论文还探讨了ASSDR在实际应用中的潜在价值，例如在图像分类、文本聚类和推荐系统等领域。由于ASSDR能够充分利用未标记数据，因此在数据标注成本高昂或难以获取的情况下，该方法具有显著的优势。总结来说，"自适应半监督降维"是针对高维数据处理的一种有效工具，ASSDR方法通过适应性地调整约束权重，实现了在有限标注信息下的高效降维，从而提高了分类和数据分析的精度。这一研究对于推动半监督学习的发展和解决实际问题具有重要的理论和实践意义。

Adaptive Semi-Supervised Dimensionality Reduction

Jia Wei

∗

, Jiabing Wang, Qianli Ma

School of Computer Science and Engineering,

South China University of Technology

Email: csjwei@scut.edu.cn

Xuan Wang

Computer Application Research Center,

Harbin Institute of Technology Shenzhen Graduate School

Email: wangxuan@insun.hit.edu.cn

Abstract—With the rapid accumulation of high dimensional

data, dimensionality reduction plays a more and more important

role in practical data processing and analysing tasks. This paper

studies semi-supervised dimensionality reduction using pairwise

constraints. In this setting, domain knowledge is given in the

form of pairwise constraints, which speciﬁes whether a pair

of instances belong to the same class (must-link constraint) or

different classes (cannot-link constraint). In this paper, a novel

semi-supervised dimensionality reduction method called Adaptive

Semi-Supervised Dimensionality Reduction (ASSDR) is proposed,

which can get the optimized low dimensional representation of the

original data by adaptively adjusting the weights of the pairwise

constraints and simultaneously optimizing the graph construc-

tion. Experiments on UCI classiﬁcation and face recognition show

that ASSDR is superior to many existing dimensionality reduction

methods.

I. INTRODUCTION

In many real world applications, such as face recognition,

information retrieval and bioinformatics, etc, one is often

confronted with high dimensional data. However, high di-

mensionality is a major cause of the practical limitations of

many pattern recognition technologies. Speciﬁcally, it has been

observed that a large number of features may actually degrade

the performance of classiﬁers if the number of training samples

is small relative to the number of the features. This is called

the ”Curse of Dimensionality” [10]. Fortunately, there might be

reason to suspect that the naturally generated high dimensional

data probably reside on a lower dimensional manifold. This

leads one to consider methods of dimensionality reduction

that allow one to represent the data in a lower dimensional

subspace.

The goal of dimensionality reduction is to reduce the

complexity of the input data while some desired intrinsic

information of the data is preserved. Two of the most popular

methods for dimensionality reduction are Principal Component

Analysis (PCA) and Linear Discriminant Analysis (LDA),

which are unsupervised and supervised respectively. PCA tries

to preserve the global covariance structure of the data in a low

dimensional projection subspace without knowing the class

labels of the data; while LDA aims to minimize the within-

class similarity and maximize the between-class similarity

simultaneously in a low dimensional projection subspace when

the class labels of the data are available.

In recent years, dimensionality reduction in semi-

supervised situation has attracted more and more attention

[16], [7]. In many real world applications such as image

classiﬁcation, web page classiﬁcation and protein function

prediction, a labeling process is costly and time-consuming; in

contrast, unlabeled examples can be easily obtained. Therefore,

in such situations, it can be beneﬁcial to incorporate the

information which is contained in unlabeled examples into a

learning problem, i.e., semi-supervised learning (SSL) should

be applied instead of supervised learning.

However, in many cases, people cannot tell which category

an instance belongs to, that is we do not know the exact label of

an instance, and what we know is the constraint information of

whether a pair of instances belong to the same class (must-link

constraint) or different classes (cannot-link constraint) [18].

The above pairwise constraint information is called ”Side In-

formation”. It can be seen that side information is more general

than label information, because we can get side information

form label information but it cannot work contrariwise [13].

So learning with side information is becoming an important

area in machine learning community.

Recently, some related works have been proposed to make

use of the pairwise constraints to extract low dimensional

structure in high dimensional data. Bar-Hillel et al. proposed

Relevant Component Analysis (RCA) which can make use of

the must-link constraints for semi-supervised dimensionality

reduction [3]. Xing et al. [20], Tang et al. [17], Yeung et al.

[22] and An et al. [1] proposed different constraints based

semi-supervised dimensionality reduction methods, which can

make use of both the must-link constraints and cannot-link

constraints. Zhang et al. proposed Semi-Supervised Dimen-

sionality Reduction (SSDR) [23] and Chen et al. used SSDR

in hyperspectral image classiﬁcation recently [8]. SSDR can

use the pairwise constraints as well as preserve the global

covariance structure of the unlabeled data in the projected low

dimensional subspace. Cevikalp et al. proposed Constrained

Locality Preserving Projections (CLPP) [5] which is the semi-

supervised version of LPP [12]. The method can make use of

the information provided by the pairwise constraints and can

also use the unlabelled data by preserving the local structure

used in LPP. Wei et al. proposed Neighborhood Preserving

based Semi-Supervised Dimensionality Reduction (NPSSDR)

[19] by using the pairwise constraints and preserving the

neighborhood structure used in LLE [14]. Baghshah et al.

used the idea of NPSSDR in metric learning and used a

heuristic search algorithm to solve the proposed constrained

trace ratio problem [2]. Davidson proposed a graph driven

constrained dimensionality reduction approach GCDR-LP for

clustering [9]. In this approach, a constraint graph is ﬁrstly

created by propagate the constraints due to transitivity and

entailment in the graph, and then the dimensionality reduction

can be conducted by the constraint graph. Yan et al. proposed

a method named Dual Subspace Projections (DSP) [21]. The

method ﬁrst integrates the must-link constraints in the kernel

space to get kernel null space and then integrates the cannot-

2014 IEEE International Conference on Data Mining Workshop

DOI 10.1109/ICDMW.2014.20

684

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