The population burden of fractures originates in women with osteopenia, not osteoporosis

Introduction : Osteoporosis is associated with increased risk for fracture. However, most postmenopausal women have bone mineral density (BMD) within the normal or osteopenic range. The aim of this study was to determine the proportion of the population burden of fragility fractures arising from women at modest risk for fracture.

Methods : We measured baseline BMD in a population-based random sample of 616 postmenopausal women aged 60–94 years and followed these individuals for a median of 5.6 years (IQR 3.9–6.5) to determine the incidence of fractures according to age, BMD and the presence of a prior fracture.

Results : Based on WHO criteria, 37.6% of the women had normal total hip BMD, 48.0% had osteopenia and 14.5% had osteoporosis. The incidence of fracture during follow-up was highest in women with osteoporosis, but only 26.9% of all fractures arose from this group; 73.1% occurred in women without osteoporosis (56.5% in women with osteopenia, 16.6% in women with normal BMD). Decreasing BMD, increasing age and prior fracture contributed independently to increased fracture risk; in a multivariate model, the relative risk for fracture increased 65% for each SD decrease in BMD (RR=1.65, 95%CI 1.32–2.05), increased 3% for every year of age (RR=1.03, 95%CI 1.01–1.06) and doubled with prevalent fracture (RR=2.01, 95% CI 1.40–2.88). A prevalent fracture increased the risk for fractures such that women with osteopenia and prevalent fracture had the same, if not greater, risk as women with osteoporosis alone.

Boosting performance for 2D linear discriminant analysis via regression

Two Dimensional Linear Discriminant Analysis (2DLDA) has received much interest in recent years. However, 2DLDA could make pairwise distances between any two classes become significantly unbalanced, which may affect its performance. Moreover 2DLDA could also suffer from the small sample size problem. Based on these observations, we propose two novel algorithms called Regularized 2DLDA and Ridge Regression for 2DLDA (RR-2DLDA). Regularized 2DLDA is an extension of 2DLDA with the introduction of a regularization parameter to deal with the small sample size problem. RR-2DLDA integrates ridge regression into Regularized 2DLDA to balance the distances among different classes after the transformation. These proposed algorithms overcome the limitations of 2DLDA and boost recognition accuracy. The experimental results on the Yale, PIE and FERET databases showed that RR-2DLDA is superior not only to 2DLDA but also other state-of-the-art algorithms.

Ridge regression for two dimensional locality preserving projection

Two Dimensional Locality Preserving Projection (2D-LPP) is a recent extension of LPP, a popular face recognition algorithm. It has been shown that 2D-LPP performs better than PCA, 2D-PCA and LPP. However, the computational cost of 2D-LPP is high. This paper proposes a novel algorithm called Ridge Regression for Two Dimensional Locality Preserving Projection (RR- 2DLPP), which is an extension of 2D-LPP with the use of ridge regression. RR-2DLPP is comparable to 2DLPP in performance whilst having a lower computational cost. The experimental results on three benchmark face data sets - the ORL, Yale and FERET databases - demonstrate the effectiveness and efficiency of RR-2DLPP compared with other face recognition algorithms such as PCA, LPP, SR, 2D-PCA and 2D-LPP.

Face recognition using kernel ridge regression

In this paper, we present novel ridge regression (RR) and kernel ridge regression (KRR) techniques for multivariate labels and apply the methods to the problem of face recognition. Motivated by the fact that the regular simplex vertices are separate points with highest degree of symmetry, we choose such vertices as the targets for the distinct individuals in recognition and apply RR or KRR to map the training face images into a face subspace where the training images from each individual will locate near their individual targets. We identify the new face image by mapping it into this face subspace and comparing its distance to all individual targets. An efficient cross-validation algorithm is also provided for selecting the regularization and kernel parameters. Experiments were conducted on two face databases and the results demonstrate that the proposed algorithm significantly outperforms the three popular linear face recognition techniques (Eigenfaces, Fisherfaces and Laplacianfaces) and also performs comparably with the recently developed Orthogonal Laplacianfaces with the advantage of computational speed. Experimental results also demonstrate that KRR outperforms RR as expected since KRR can utilize the nonlinear structure of the face images. Although we concentrate on face recognition in this paper, the proposed method is general and may be applied for general multi-category classification problems.