Effective Discriminative Feature Selection with Non-trivial Solutions

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation based dimensionality reduction method Linear Discriminant Analysis (LDA) and sparsity regularization. We impose row sparsity on the transformation matrix of LDA through ${\ell}_{2,1}$-norm regularization to achieve feature selection, and the resultant formulation optimizes for selecting the most discriminative features and removing the redundant ones simultaneously. The formulation is extended to the ${\ell}_{2,p}$-norm regularized case: which is more likely to offer better sparsity when $0<p<1$. Thus the formulation is a better approximation to the feature selection problem. An efficient algorithm is developed to solve the ${\ell}_{2,p}$-norm based optimization problem and it is proved that the algorithm converges when $0<p\le 2$. Systematical experiments are conducted to understand the work of the proposed method. Promising experimental results on various types of real-world data sets demonstrate the effectiveness of our algorithm

Mandibular reconstruction with vascularised bone flaps: a systematic review over 25 years

To explore the techniques for mandibular reconstruction with composite free flaps and their outcomes, we systematically reviewed reports published between 1990 and 2015. A total of 9499 mandibular defects were reconstructed with 6178 fibular, 1380 iliac crest, 1127 composite radial, 709 scapular, 63 serratus anterior and rib, 32 metatarsal, and 10 lateral arm flaps including humerus. The failure rate was higher for the iliac crest (6.2%, 66/1059) than for fibular, radial, and scapular flaps combined (3.4%, 202/6018) (p<0.001). We evaluated rates of osteotomy, non-union, and fistulas. Implant-retained prostheses were used most often for rehabilitation after reconstruction with iliac crest (44%, 100/229 compared with 26%, 605/2295 if another flap was used) (p<0.001). There were no apparent changes in the choice of flap or in the complications reported. Although we were able to show some significant differences relating to the types of flap used, we were disappointed to find that fundamental outcomes such as the need for osteotomy, and rates of non-union and fistulas were under-reported. This review shows the need for more comprehensive and consistent reporting of outcomes to enable the comparison of different techniques for similar defects

Evaluation of scaling invariance embedded in short time series.

Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length ~10(2). Calculations with specified Hurst exponent values of 0.2,0.3,...,0.9 show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias (≤0.03) and sharp confidential interval (standard deviation ≤0.05). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records

Joint Embedding Learning and Sparse Regression: A Framework for Unsupervised Feature Selection

Feature selection has aroused considerable research interests during the last few decades. Traditional learning-based feature selection methods separate embedding learning and feature ranking. In this paper, we propose a novel unsupervised feature selection framework, termed as the joint embedding learning and sparse regression (JELSR), in which the embedding learning and sparse regression are jointly performed. Specifically, the proposed JELSR joins embedding learning with sparse regression to perform feature selection. To show the effectiveness of the proposed framework, we also provide a method using the weight via local linear approximation and adding the l(2,1)-norm regularization, and design an effective algorithm to solve the corresponding optimization problem. Furthermore, we also conduct some insightful discussion on the proposed feature selection approach, including the convergence analysis, computational complexity, and parameter determination. In all, the proposed framework not only provides a new perspective to view traditional methods but also evokes some other deep researches for feature selection. Compared with traditional unsupervised feature selection methods, our approach could integrate the merits of embedding learning and sparse regression. Promising experimental results on different kinds of data sets, including image, voice data and biological data, have validated the effectiveness of our proposed algorithm