The result of the literature.

In bold–the best performance.</p

Feature Selection and Cancer Classification via Sparse Logistic Regression with the Hybrid L_{1/2 +2} Regularization

<div><p>Cancer classification and feature (gene) selection plays an important role in knowledge discovery in genomic data. Although logistic regression is one of the most popular classification methods, it does not induce feature selection. In this paper, we presented a new hybrid L_{1/2 +2} regularization (HLR) function, a linear combination of L_1/2 and L₂ penalties, to select the relevant gene in the logistic regression. The HLR approach inherits some fascinating characteristics from L_1/2 (sparsity) and L₂ (grouping effect where highly correlated variables are in or out a model together) penalties. We also proposed a novel univariate HLR thresholding approach to update the estimated coefficients and developed the coordinate descent algorithm for the HLR penalized logistic regression model. The empirical results and simulations indicate that the proposed method is highly competitive amongst several state-of-the-art methods.</p></div

Contour plots (two-dimensional) for the regularization methods.

<p>The regularization parameters are <i>λ</i> = 1 and <i>α</i> = 0.2 for the HLR method.</p

The most frequently selected 10 genes found by the five sparse logistic regression methods from the lung cancer dataset.

<p>The most frequently selected 10 genes found by the five sparse logistic regression methods from the lung cancer dataset.</p

Real datasets used in this paper.

<p>Real datasets used in this paper.</p

Mean results of empirical datasets.

<p>In bold–the best performance.</p

The validation results of the classifiers based on the top rank selected genes from lung cancer dataset.

<p>In bold–the best performance.</p

The performance of the AUC from ROC analyzes of each method on prostate, lymphoma and lung cancer datasets.

<p>The performance of the AUC from ROC analyzes of each method on prostate, lymphoma and lung cancer datasets.</p

Mean results of the simulation.

<p>In bold–the best performance amongst all the methods.</p

Homogeneous and Real Super Tough Multi-Bond Network Hydrogels Created through a Controllable Metal Ion Permeation Strategy

Poly­(acrylic acid) (PAA) hydrogels with a multi-bond network composed of sparse chemical cross-links and carboxyl-Fe3+ coordination are prepared through a controllable permeation strategy utilizing ferric citrate (FeCA). The existing strategies that directly soak PAA hydrogels in Fe3+ solutions usually induce an inhomogeneous network with densely cross-linked shells and uncertain water content of the hydrogels, which brings about ambiguity when investigating strengthening mechanisms because water content significantly affects the mechanical properties of hydrogels. Herein, the controllable permeation of Fe3+ into PAA networks based on the competition between citric acid (CA)-Fe3+ chelation and PAA-Fe3+ coordination guarantees sustained release of Fe3+, facilitating homogeneous distribution of ionic cross-links and a certain water content. The obtained hydrogels exhibit excellent and balanced mechanical properties (high tensile strength of 3.28 to 6.95 MPa with large elongations at break of 1400 to 780% when water content decreases from 80 to 50 wt %). The real robust tensile strength of this hydrogel originates from the effective energy dissipation of the homogeneous PAA-Fe3+ cross-links, and the high water content ensures a large elongation at break. Furthermore, the hydrogel also has pH-responsive and shape-memory properties