Visual object clustering via mixed-norm regularization

Many vision problems deal with high-dimensional data, such as motion segmentation and face clustering. However, these high-dimensional data usually lie in a low-dimensional structure. Sparse representation is a powerful principle for solving a number of clustering problems with high-dimensional data. This principle is motivated from an ideal modeling of data points according to linear algebra theory. However, real data in computer vision are unlikely to follow the ideal model perfectly. In this paper, we exploit the mixed norm regularization for sparse subspace clustering. This regularization term is a convex combination of the l1norm, which promotes sparsity at the individual level and the block norm l2/1 which promotes group sparsity. Combining these powerful regularization terms will provide a more accurate modeling, subsequently leading to a better solution for the affinity matrix used in sparse subspace clustering. This could help us achieve better performance on motion segmentation and face clustering problems. This formulation also caters for different types of data corruptions. We derive a provably convergent algorithm based on the alternating direction method of multipliers (ADMM) framework, which is computationally efficient, to solve the formulation. We demonstrate that this formulation outperforms other state-of-arts on both motion segmentation and face clustering.

Fitting aggregation functions to data: part I-linearization and regularization

The use of supervised learning techniques for fitting weights and/or generator functions of weighted quasi-arithmetic means – a special class of idempotent and nondecreasing aggregation functions – to empirical data has already been considered in a number of papers. Nevertheless, there are still some important issues that have not been discussed in the literature yet. In the first part of this two-part contribution we deal with the concept of regularization, a quite standard technique from machine learning applied so as to increase the fit quality on test and validation data samples. Due to the constraints on the weighting vector, it turns out that quite different methods can be used in the current framework, as compared to regression models. Moreover, it is worth noting that so far fitting weighted quasi-arithmetic means to empirical data has only been performed approximately, via the so-called linearization technique. In this paper we consider exact solutions to such special optimization tasks and indicate cases where linearization leads to much worse solutions.

Mathematical modelling of the refractive index reconstruction through global optimization

We examine a mathematical model of non-destructive testing of planar waveguides, based on numerical solution of a nonlinear integral equation. Such problem is ill-posed, and the method of Tikhonov regularization is applied. To minimize Tikhonov functional, and find the parameters of the waveguide, we use two new optimization methods: the cutting angle method of global optimization, and the discrete gradient method of nonsmooth local optimization. We examine how the noise in the experimental data influences the solution, and how the regularization parameter has to be chosen. We show that even with significant noise in the data, the numerical solution is of high accuracy, and the method can be used to process real experimental da.ta..

Planar waveguide refractive index profile reconstruction using global optimization

The approach taken here of reconstruction of the refractive index profile of planar waveguides involves solving a non-linear integral equation with Tikhonov regularization. Using global optimization with the new cutting angle and discrete gradient methods has yielded an acceptable reconstruction, even in the presence of significant noise in the data.

Robust ODF smoothing for accurate estimation of fiber orientation

Q-ball imaging was presented as a model free, linear and multimodal diffusion sensitive approach to reconstruct diffusion orientation distribution function (ODF) using diffusion weighted MRI data. The ODFs are widely used to estimate the fiber orientations. However, the smoothness constraint was proposed to achieve a balance between the angular resolution and noise stability for ODF constructs. Different regularization methods were proposed for this purpose. However, these methods are not robust and quite sensitive to the global regularization parameter. Although, numerical methods such as L-curve test are used to define a globally appropriate regularization parameter, it cannot serve as a universal value suitable for all regions of interest. This may result in over smoothing and potentially end up in neglecting an existing fiber population. In this paper, we propose to include an interpolation step prior to the spherical harmonic decomposition. This interpolation based approach is based on Delaunay triangulation provides a reliable, robust and accurate smoothing approach. This method is easy to implement and does not require other numerical methods to define the required parameters. Also, the fiber orientations estimated using this approach are more accurate compared to other common approaches.

A novel monotonic fixed-point algorithm for l1-regularized least square vector and matrix problem

Least square problem with l₁ regularization has been proposed as a promising method for sparse signal reconstruction (e.g., basis pursuit de-noising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as l₁-regularized least-square program (LSP). In this paper, we propose a novel monotonic fixed point method to solve large-scale l₁-regularized LSP. And we also prove the stability and convergence of the proposed method. Furthermore we generalize this method to least square matrix problem and apply it in nonnegative matrix factorization (NMF). The method is illustrated on sparse signal reconstruction, partner recognition and blind source separation problems, and the method tends to convergent faster and sparser than other l₁-regularized algorithms.

Regularized nonnegative shared subspace learning

Joint modeling of related data sources has the potential to improve various data mining tasks such as transfer learning, multitask clustering, information retrieval etc. However, diversity among various data sources might outweigh the advantages of the joint modeling, and thus may result in performance degradations. To this end, we propose a regularized shared subspace learning framework, which can exploit the mutual strengths of related data sources while being immune to the effects of the variabilities of each source. This is achieved by further imposing a mutual orthogonality constraint on the constituent subspaces which segregates the common patterns from the source specific patterns, and thus, avoids performance degradations. Our approach is rooted in nonnegative matrix factorization and extends it further to enable joint analysis of related data sources. Experiments performed using three real world data sets for both retrieval and clustering applications demonstrate the benefits of regularization and validate the effectiveness of the model. Our proposed solution provides a formal framework appropriate for jointly analyzing related data sources and therefore, it is applicable to a wider context in data mining.

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.

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.

Robust single-hidden layer feedforward network-based pattern classifier

In this paper, a new robust single-hidden layer feedforward network (SLFN)-based pattern classifier is developed. It is shown that the frequency spectrums of the desired feature vectors can be specified in terms of the discrete Fourier transform (DFT) technique. The input weights of the SLFN are then optimized with the regularization theory such that the error between the frequency components of the desired feature vectors and the ones of the feature vectors extracted from the outputs of the hidden layer is minimized. For the linearly separable input patterns, the hidden layer of the SLFN plays the role of removing the effects of the disturbance from the noisy input data and providing the linearly separable feature vectors for the accurate classification. However, for the nonlinearly separable input patterns, the hidden layer is capable of assigning the DFTs of all feature vectors to the desired positions in the frequencydomain such that the separability of all nonlinearly separable patterns are maximized. In addition, the output weights of the SLFN are also optimally designed so that both the empirical and the structural risks are well balanced and minimized in a noisy environment. Two simulation examples are presented to show the excellent performance and effectiveness of the proposed classification scheme.

Modeling dual role preferences for trust-aware recommendation

Unlike in general recommendation scenarios where a user has only a single role, users in trust rating network, e.g. Epinions, are associated with two different roles simultaneously: as a truster and as a trustee. With different roles, users can show distinct preferences for rating items, which the previous approaches do not involve. Moreover, based on explicit single links between two users, existing methods can not capture the implicit correlation between two users who are similar but not socially connected. In this paper, we propose to learn dual role preferences (truster/trustee-specific preferences) for trust-aware recommendation by modeling explicit interactions (e.g., rating and trust) and implicit interactions. In particular, local links structure of trust network are exploited as two regularization terms to capture the implicit user correlation, in terms of truster/trustee-specific preferences. Using a real-world and open dataset, we conduct a comprehensive experimental study to investigate the performance of the proposed model, RoRec. The results show that RoRec outperforms other trust-aware recommendation approaches, in terms of prediction accuracy. Copyright 2014 ACM.

Improved risk predictions via sparse imputation of patient conditions in electronic medical records

Electronic Medical Records (EMR) are increasingly used for risk prediction. EMR analysis is complicated by missing entries. There are two reasons - the “primary reason for admission” is included in EMR, but the co-morbidities (other chronic diseases) are left uncoded, and, many zero values in the data are accurate, reflecting that a patient has not accessed medical facilities. A key challenge is to deal with the peculiarities of this data - unlike many other datasets, EMR is sparse, reflecting the fact that patients have some, but not all diseases. We propose a novel model to fill-in these missing values, and use the new representation for prediction of key hospital events. To “fill-in” missing values, we represent the feature-patient matrix as a product of two low rank factors, preserving the sparsity property in the product. Intuitively, the product regularization allows sparse imputation of patient conditions reflecting common comorbidities across patients. We develop a scalable optimization algorithm based on Block coordinate descent method to find an optimal solution. We evaluate the proposed framework on two real world EMR cohorts: Cancer (7000 admissions) and Acute Myocardial Infarction (2652 admissions). Our result shows that the AUC for 3 months admission prediction is improved significantly from (0.741 to 0.786) for Cancer data and (0.678 to 0.724) for AMI data. We also extend the proposed method to a supervised model for predicting of multiple related risk outcomes (e.g. emergency presentations and admissions in hospital over 3, 6 and 12 months period) in an integrated framework. For this model, the AUC averaged over outcomes is improved significantly from (0.768 to 0.806) for Cancer data and (0.685 to 0.748) for AMI data.

Graph-induced restricted Boltzmann machines for document modeling

Discovering knowledge from unstructured texts is a central theme in data mining and machine learning. We focus on fast discovery of thematic structures from a corpus. Our approach is based on a versatile probabilistic formulation – the restricted Boltzmann machine (RBM) –where the underlying graphical model is an undirected bipartite graph. Inference is efficient document representation can be computed with a single matrix projection, making RBMs suitable for massive text corpora available today. Standard RBMs, however, operate on bag-of-words assumption, ignoring the inherent underlying relational structures among words. This results in less coherent word thematic grouping. We introduce graph-based regularization schemes that exploit the linguistic structures, which in turn can be constructed from either corpus statistics or domain knowledge. We demonstrate that the proposed technique improves the group coherence, facilitates visualization, provides means for estimation of intrinsic dimensionality, reduces overfitting, and possibly leads to better classification accuracy.