Semi-Supervised Fuzzy-Rough Feature Selection

With the continued and relentless growth in dataset sizes in recent times, feature or attribute selection has become a necessary step in tackling the resultant intractability. Indeed, as the number of dimensions increases, the number of corresponding data instances required in order to generate accurate models increases exponentially. Fuzzy-rough set-based feature selection techniques offer great flexibility when dealing with real-valued and noisy data; however, most of the current approaches focus on the supervised domain where the data object labels are known. Very little work has been carried out using fuzzy-rough sets in the areas of unsupervised or semi-supervised learning. This paper proposes a novel approach for semi-supervised fuzzy-rough feature selection where the object labels in the data may only be partially present. The approach also has the appealing property that any generated subsets are also valid (super)reducts when the whole dataset is labelled. The experimental evaluation demonstrates that the proposed approach can generate stable and valid subsets even when up to 90 % of the data object labels are missing.

1. 1.

   When \(B = \{a\}\), i.e., B is a singleton, \(R_a\) is written rather than \(R_{\{a\}}\).

2. 2.

   A t-norm \(\mathcal {T}\) is an increasing, commutative, associative \([0,1]^2 \rightarrow [0,1]\) mapping satisfying \(\mathcal {T}(x,1) = x\) for x in [0, 1].

3. 3.

   An implicator \(\mathcal {I}\) is a \([0,1]^2 \rightarrow [0,1]\) mapping that is decreasing in its first and increasing in its second argument, satisfying \(\mathcal {I}(0,0)=\mathcal {I}(0,1)=\mathcal {I}(1,1)=1\) and \(\mathcal {I}(1,0)=0\).

Neil Mac Parthaláin would like to acknowledge the financial support for this research through NISCHR (National Institute for Social Care and Health Research) Wales, Grant reference: RFS-12-37. Sarah Vluymans is supported by the Special Research Fund (BOF) of Ghent University. Chris Cornelis was partially supported by the Spanish Ministry of Science and Technology under the project TIN2011-28488 and the Andalusian Research Plans P11-TIC-7765, P10-TIC-6858 and P12-TIC-2958.

Authors and Affiliations

1. Department of Computer Science, Aberystwyth University, Aberystwyth, Ceredigion, Wales, UK

   Richard Jensen & Neil Mac Parthaláin

2. Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium

   Sarah Vluymans & Chris Cornelis

3. VIB Inflammation Research Center, Zwijnaarde, Belgium

   Sarah Vluymans & Yvan Saeys

4. Department of Computer Science and AI CITIC-UGR, University of Granada, Granada, Spain

   Chris Cornelis

5. Department of Respiratory Medicine, Ghent University, Ghent, Belgium

   Yvan Saeys

Corresponding author

Correspondence to Richard Jensen .

Editors and Affiliations

1. University of Regina, Regina, SK, Canada

   Yiyu Yao

2. Tianjin University, Tianjin, China

   Qinghua Hu

3. Chongqing University of Posts and Telecommunications, Chongqing, China

   Hong Yu

4. University of Kansas, Lawrence, KS, USA

   Jerzy W. Grzymala-Busse

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