Title
Semi-Supervised Feature Selection via Sparse Rescaled Linear Square Regression
Abstract
With the rapid increase of the data size, it has increasing demands for selecting features by exploiting both labeled and unlabeled data. In this paper, we propose a novel semi-supervised embedded feature selection method. The new method extends the least square regression model by rescaling the regression coefficients in the least square regression with a set of scale factors, which is used for evaluating the importance of features. An iterative algorithm is proposed to optimize the new model. It has been proved that solving the new model is equivalent to solving a sparse model with a flexible and adaptable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2,p}$</tex-math><alternatives><mml:math><mml:msub><mml:mi>ℓ</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href="chen-ieq1-2879797.gif"/></alternatives></inline-formula> norm regularization. Moreover, the optimal solution of scale factors provides a theoretical explanation for why we can use <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lbrace \left\Vert \mathbf {w}^{1} \right\Vert _{2},\ldots, \left\Vert \mathbf {w}^{d} \right\Vert _{2}\rbrace$</tex-math><alternatives><mml:math><mml:mrow><mml:mo>{</mml:mo><mml:msub><mml:mfenced close="∥" open="∥" separators=""><mml:msup><mml:mi mathvariant="bold">w</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:mfenced><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>...</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mfenced close="∥" open="∥" separators=""><mml:msup><mml:mi mathvariant="bold">w</mml:mi><mml:mi>d</mml:mi></mml:msup></mml:mfenced><mml:mn>2</mml:mn></mml:msub><mml:mo>}</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="chen-ieq2-2879797.gif"/></alternatives></inline-formula> to evaluate the importance of features. Experimental results on eight benchmark data sets show the superior performance of the proposed method.
Year
DOI
Venue
2020
10.1109/TKDE.2018.2879797
IEEE Transactions on Knowledge and Data Engineering
Keywords
Field
DocType
Feature extraction,Computational complexity,Laplace equations,Knowledge discovery,Data engineering,Iterative methods,Adaptation models
Least squares,Data mining,Applied mathematics,Data set,Regression,Feature selection,Iterative method,Regression analysis,Computer science,Regularization (mathematics),Linear regression
Journal
Volume
Issue
ISSN
32
1
1041-4347
Citations 
PageRank 
References 
8
0.42
0
Authors
4
Name
Order
Citations
PageRank
Xiaojun Chen11298107.51
Guowen Yuan2263.05
Feiping Nie37061309.42
Zhong Ming41377106.41