Eunwoo Kim

Real-time navigation in crowded dynamic environments using Gaussian process motion control

In this paper, we propose a novel Gaussian process motion controller that can navigate through a crowded dynamic environment. The proposed motion controller predicts future trajectories of pedestrians using an autoregressive Gaussian process motion model (AR-GPMM) from the partially-observable egocentric view of a robot and controls a robot using an autoregressive Gaussian process motion controller (AR-GPMC) based on predicted pedestrian trajectories. The performance of the proposed method is extensively evaluated in simulation and validated experimentally using a Pioneer 3DX mobile robot with a Microsoft Kinect sensor. In particular, the proposed method shows over 68% improvement on the collision rate compared to a reactive planner and vector field histogram (VFH).

Efficient

Low-rank matrix approximation plays an important role in the area of computer vision and image processing. Most of the conventional low-rank matrix approximation methods are based on the l2-norm (Frobenius norm) with principal component analysis (PCA) being the most popular among them. However, this can give a poor approximation for data contaminated by outliers (including missing data), because the l2-norm exaggerates the negative effect of outliers. Recently, to overcome this problem, various methods based on the l1-norm, such as robust PCA methods, have been proposed for low-rank matrix approximation. Despite the robustness of the methods, they require heavy computational effort and substantial memory for high-dimensional data, which is impractical for realworld problems. In this paper, we propose two efficient low-rank factorization methods based on the l1-norm that find proper projection and coefficient matrices using the alternating rectified gradient method. The proposed methods are applied to a number of low-rank matrix approximation problems to demonstrate their efficiency and robustness. The experimental results show that our proposals are efficient in both execution time and reconstruction performance unlike other state-of-the-art methods.

l_{1}

There is a growing interest in smart homes and predicting behaviors of inhabitants is a key element for the success of smart home services. In this paper, we propose two algorithms, DBN-ANN and DBN-R, based on the deep learning framework for predicting various activities in a home. We also address drawbacks of contrastive divergence, a widely used learning method for restricted Boltzmann machines, and propose an efficient online learning algorithm based on bootstrapping. From experiments using home activity datasets, we show that our proposed prediction algorithms outperform existing methods, such as a nonlinear SVM and k-means, in terms of prediction accuracy of newly activated sensors. In particular, DBN-R shows an accuracy of 43.9% (51.8%) for predicting newly activated sensors based on MIT home dataset 1 (dataset 2), while previous work based on the n-gram algorithm has shown an accuracy of 39% (43%) on the same dataset.

-Norm-Based Low-Rank Matrix Approximations for Large-Scale Problems Using Alternating Rectified Gradient Method

Learning a low-dimensional structure plays an important role in computer vision. Recently, a new family of methods, such as l1 minimization and robust principal component analysis, has been proposed for low-rank matrix approximation problems and shown to be robust against outliers and missing data. But these methods often require heavy computational load and can fail to find a solution when highly corrupted data are presented. In this paper, an elastic-net regularization based low-rank matrix factorization method for subspace learning is proposed. The proposed method finds a robust solution efficiently by enforcing a strong convex constraint to improve the algorithms stability while maintaining the low-rank property of the solution. It is shown that any stationary point of the proposed algorithm satisfies the Karush-Kuhn-Tucker optimality conditions. The proposed method is applied to a number of low-rank matrix approximation problems to demonstrate its efficiency in the presence of heavy corruptions and to show its effectiveness and robustness compared to the existing methods.

Human behavior prediction for smart homes using deep learning

In this paper, we propose a novel regression method that can incorporate both positive and negative training data into a single regression framework. In detail, a leveraged kernel function for non-stationary Gaussian process regression is proposed. With this new kernel function, we can vary the correlation betwen two inputs in both positive and negative directions by adjusting leverage parameters. By using this property, the resulting leveraged non-stationary Gaussian process regression can anchor the regressor to the positive data while avoiding the negative data. We first prove the positive semi-definiteness of the leveraged kernel function using Bochners theorem. Then, we apply the leveraged non-stationary Gaussian process regression to a real-time motion control problem. In this case, the positive data refer to what to do and the negative data indicate what not to do. The results show that the controller using both positive and negative data outperforms the controller using positive data only in terms of the collision rate given training sets of the same size.

Elastic-net regularization of singular values for robust subspace learning

Abstract In this paper, we propose a nonparametric motion controller using Gaussian process regression for autonomous navigation in a dynamic environment. Particularly, we focus on its applicability to low-cost mobile robot platforms with low-performance processors. The proposed motion controller predicts future trajectories of pedestrians using the partially-observable egocentric view of a robot and controls a robot using both observed and predicted trajectories. Furthermore, a hierarchical motion controller is proposed by dividing the controller into multiple sub-controllers using a mixture-of-experts framework to further alleviate the computational cost. We also derive an efficient method to approximate the upper bound of the learning curve of Gaussian process regression, which can be used to determine the required number of training samples for the desired performance. The performance of the proposed method is extensively evaluated in simulations and validated experimentally using a Pioneer 3DX mobile robot with two Microsoft Kinect sensors. In particular, the proposed baseline and hierarchical motion controllers show over 65 % and 51 % improvements over a reactive planner and predictive vector field histogram, respectively, in terms of the collision rate.

Leveraged non-stationary Gaussian process regression for autonomous robot navigation

Low-rank matrix factorization plays an important role in the areas of pattern recognition, computer vision, and machine learning. Recently, a new family of methods, such as l1-norm minimization and robust PCA, has been proposed for low-rank subspace analysis problems and has shown to be robust against outliers and missing data. But these methods suffer from heavy computation loads and can fail to find a solution when highly corrupted data are presented. In this paper, a robust orthogonal matrix approximation method using fixed-rank factorization is proposed. The proposed method finds a robust solution efficiently using orthogonality and smoothness constraints. The proposed method is also extended to handle the rank uncertainty issue by a rank estimation strategy for practical real-world problems. The proposed method is applied to a number of low-rank matrix approximation problems and experimental results show that the proposed method is highly accurate, fast, and efficient compared to the existing methods. HighlightsThis paper considers a subspace learning problem in the presence of corruptions.The proposed method finds a robust solution using orthogonality and smoothness constraints.The proposed method can handle missing or unknown entries as well as outliers.The proposed method is extended to handle the rank uncertainty issue.We demonstrate that the proposed method is robust for various subspace learning problems.

Real-time nonparametric reactive navigation of mobile robots in dynamic environments

This paper considers the problem of modeling complex motions of pedestrians in a crowded environment. A number of methods have been proposed to predict the motion of a pedestrian or an object. However, it is still difficult to make a good prediction due to challenges, such as the complexity of pedestrian motions and outliers in a training set. This paper addresses these issues by proposing a robust autoregressive motion model based on Gaussian process regression using l1-norm based low-rank kernel matrix approximation, called PCGP-l1. The proposed method approximates a kernel matrix assuming that the kernel matrix can be well represented using a small number of dominating principal components, eliminating erroneous data. The proposed motion model is robust against outliers present in a training set and can reliably predict the motion of a pedestrian, such that it can be used by a robot for safe navigation in a crowded environment. The proposed method is applied to a number of regression and motion prediction problems to demonstrate its robustness and efficiency. The experimental results show that the proposed method considerably improves the motion prediction rate compared to other Gaussian process regression methods.

Robust orthogonal matrix factorization for efficient subspace learning

Recently, finding the low-dimensional structure of high-dimensional data has gained much attention. Given a set of data points sampled from a single subspace or a union of subspaces, the goal is to learn or capture the underlying subspace structure of the data set. In this paper, we propose elastic-net subspace representation, a new subspace representation framework using elastic-net regularization of singular values. Due to the strong convexity enforced by elastic-net, the proposed method is more stable and robust in the presence of heavy corruptions compared with existing lasso-type rank minimization approaches. For discovering a single low-dimensional subspace, we propose a computationally efficient low-rank factorization algorithm, called FactEN, using a property of the nuclear norm and the augmented Lagrangian method. Then, ClustEN is proposed to handle the general case, in which the data samples are drawn from a union of multiple subspaces, for joint subspace clustering and estimation. The proposed algorithms are applied to a number of subspace representation problems to evaluate the robustness and efficiency under various noisy conditions, and experimental results show the benefits of the proposed method compared with existing methods.Recently, finding the low-dimensional structure of high-dimensional data has gained much attention. Given a set of data points sampled from a single subspace or a union of subspaces, the goal is to learn or capture the underlying subspace structure of the data set. In this paper, we propose elastic-net subspace representation, a new subspace representation framework using elastic-net regularization of singular values. Due to the strong convexity enforced by elastic-net, the proposed method is more stable and robust in the presence of heavy corruptions compared with existing lasso-type rank minimization approaches. For discovering a single low-dimensional subspace, we propose a computationally efficient low-rank factorization algorithm, called FactEN, using a property of the nuclear norm and the augmented Lagrangian method. Then, ClustEN is proposed to handle the general case, in which the data samples are drawn from a union of multiple subspaces, for joint subspace clustering and estimation. The proposed algorithms are applied to a number of subspace representation problems to evaluate the robustness and efficiency under various noisy conditions, and experimental results show the benefits of the proposed method compared with existing methods.

A robust autoregressive gaussian process motion model using l1-norm based low-rank kernel matrix approximation

This paper considers the problem of approximating a kernel matrix in an autoregressive Gaussian process regression (AR-GP) in the presence of measurement noises or natural errors for modeling complex motions of pedestrians in a crowded environment. While a number of methods have been proposed to robustly predict future motions of humans, it still remains as a difficult problem in the presence of measurement noises. This paper addresses this issue by proposing a structured low-rank matrix approximation method using nuclear-norm regularized l1-norm minimization in AR-GP for robust motion prediction of dynamic obstacles. The proposed method approximates a kernel matrix by finding an orthogonal basis using low-rank symmetric positive semi-definite matrix approximation assuming that a kernel matrix can be well represented by a small number of dominating basis vectors. The proposed method is suitable for predicting the motion of a pedestrian, such that it can be used for safe autonomous robot navigation in a crowded environment. The proposed method is applied to well-known regression and motion prediction problems to demonstrate its robustness and excellent performance compared to existing approaches.