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Table Of Integrals Series And Products

On robust estimation of the location parameter

Real and Complex Analysis

In the real world, a realistic setting for computer vision or multimedia recognition problems is that we have some classes containing lots of training data and many classes contain a small amount of training data. Therefore, how to use frequent classes to help learning rare classes for which it is harder to collect the training data is an open question. Learning with Shared Information is an emerging topic in machine learning, computer vision and multimedia analysis. There are different level of components that can be shared during concept modeling and machine learning stages, such as sharing generic object parts, sharing attributes, sharing transformations, sharing regularization parameters and sharing training examples, etc. Regarding the specific methods, multi-task learning, transfer learning and deep learning can be seen as using different strategies to share information. These learning with shared information methods are very effective in solving real-world large-scale problems. This special issue aims at gathering the recent advances in learning with shared information methods and their applications in computer vision and multimedia analysis. Both state-of-the-art works, as well as literature reviews, are welcome for submission. Papers addressing interesting real-world computer vision and multimedia applications are especially encouraged. Topics of interest include, but are not limited to:  • Multi-task learning or transfer learning for large-scale computer vision and multimedia analysis • Deep learning for large-scale computer vision and multimedia analysis • Multi-modal approach for large-scale computer vision and multimedia analysis • Different sharing strategies, e.g., sharing generic object parts, sharing attributes, sharing transformations, sharing regularization parameters and sharing training examples, • Real-world computer vision and multimedia applications based on learning with shared information, e.g., event detection, object recognition, object detection, action recognition, human head pose estimation, object tracking, location-based services, semantic indexing. • New datasets and metrics to evaluate the benefit of the proposed sharing ability for the specific computer vision or multimedia problem. • Survey papers regarding the topic of learning with shared information.  Authors who are unsure whether their planned submission is in scope may contact the guest editors prior to the submission deadline with an abstract, in order to receive feedback.

IEEE transactions on pattern analysis and machine intelligence

Matrix Differential Calculus with Applications in Statistics and Econometrics

We propose a novel 6-degree-of-freedom (DoF) visual simultaneous localization and mapping (SLAM) method based on the structural regularity of man-made building environments. The idea is that we use the building structure lines as features for localization and mapping. Unlike other line features, the building structure lines encode the global orientation information that constrains the heading of the camera over time, eliminating the accumulated orientation errors and reducing the position drift in consequence. We extend the standard extended Kalman filter visual SLAM method to adopt the building structure lines with a novel parameterization method that represents the structure lines in dominant directions. Experiments have been conducted in both synthetic and real-world scenes. The results show that our method performs remarkably better than the existing methods in terms of position error and orientation error. In the test of indoor scenes of the public RAWSEEDS data sets, with the aid of a wheel odometer, our method produces bounded position errors about 0.79 m along a 967-m path although no loop-closing algorithm is applied.

StructSLAM: Visual SLAM With Building Structure Lines

In the past decade, sparse and low-rank recovery has drawn much attention in many areas such as signal/image processing, statistics, bioinformatics, and machine learning. To achieve sparsity and/or low-rankness inducing, the $\ell _{1}$ norm and nuclear norm are of the most popular regularization penalties due to their convexity. While the $\ell _{1}$ and nuclear norm are convenient as the related convex optimization problems are usually tractable, it has been shown in many applications that a nonconvex penalty can yield significantly better performance. In recent, nonconvex regularization-based sparse and low-rank recovery is of considerable interest and it in fact is a main driver of the recent progress in nonconvex and nonsmooth optimization. This paper gives an overview of this topic in various fields in signal processing, statistics, and machine learning, including compressive sensing, sparse regression and variable selection, sparse signals separation, sparse principal component analysis (PCA), large covariance and inverse covariance matrices estimation, matrix completion, and robust PCA. We present recent developments of nonconvex regularization based sparse and low-rank recovery in these fields, addressing the issues of penalty selection, applications and the convergence of nonconvex algorithms. Code is available at https://github.com/FWen/ncreg.git .

A Survey on Nonconvex Regularization-Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning

In this paper, an improved indoor localization method based on smartphone inertial sensors is presented. Pedestrian dead reckoning (PDR), which determines the relative location change of a pedestrian without additional infrastructure supports, is combined with a floor plan for a pedestrian positioning in our work. To address the challenges of low sampling frequency and limited processing power in smartphones, reliable and efficient PDR algorithms have been proposed. A robust step detection technique leaves out the preprocessing of raw signal and reduces complex computation. Given the fact that the precision of the stride length estimation is influenced by different pedestrians and motion modes, an adaptive stride length estimation algorithm based on the motion mode classification is developed. Heading estimation is carried out by applying the principal component analysis (PCA) to acceleration measurements projected to the global horizontal plane, which is independent of the orientation of a smartphone. In addition, to eliminate the sensor drift due to the inaccurate distance and direction estimations, a particle filter is introduced to correct the drift and guarantee the localization accuracy. Extensive field tests have been conducted in a laboratory building to verify the performance of proposed algorithm. A pedestrian held a smartphone with arbitrary orientation in the tests. Test results show that the proposed algorithm can achieve significant performance improvements in terms of efficiency, accuracy and reliability.

An improved indoor localization method using smartphone inertial sensors

This paper addresses the issue of robust sparse recovery in compressive sensing (CS) in the presence of impulsive measurement noise. Recently, robust data-fitting models, such as $\ell _1$ -norm, Lorentzian-norm, and Huber penalty function, have been employed to replace the popular $\ell _2$ -norm loss model to gain more robust performance. In this paper, we propose a robust formulation for sparse recovery using the generalized $\ell _p$ -norm with $0\leq p as the metric for the residual error. To solve this formulation efficiently, we develop an alternating direction method (ADM) via incorporating the proximity operator of $\ell _p$ -norm functions into the framework of augmented Lagrangian methods. Furthermore, to derive a convergent method for the nonconvex case of $p 1, a smoothing strategy has been employed. The convergence conditions of the proposed algorithm have been analyzed for both the convex and nonconvex cases. The new algorithm has been compared with some state-of-the-art robust algorithms via numerical simulations to show its improved performance in highly impulsive noise.

Robust Sparse Recovery in Impulsive Noise via $\ell _p$ -$\ell _1$ Optimization

Magnetometer and inertial sensors are widely used for orientation estimation. Magnetometer usage is often troublesome, as it is prone to be interfered by onboard or ambient magnetic disturbance. The onboard soft-iron material distorts not only the magnetic field, but also the magnetometer sensor frame coordinate and the cross-sensor misalignment relative to inertial sensors. It is desirable to conveniently put magnetic and inertial sensors information in a common frame. Existing methods either split the problem into successive intrinsic and cross-sensor calibrations, or rely on stationary accelerometer measurements which are infeasible in dynamic conditions. This brief formulates the magnetometer calibration and alignment to inertial sensors as a state estimation problem, and collectively solves the magnetometer intrinsic and cross-sensor calibrations, as well as the gyroscope bias estimation. Sufficient conditions are derived for the problem to be globally observable, even when no accelerometer information is used at all. An extended Kalman filter is designed to implement the state estimation and comprehensive test data results show the superior performance of the proposed approach. It is immune to acceleration disturbance and applicable potentially in any dynamic conditions.

Peilin Liu

Papers

StructSLAM: Visual SLAM With Building Structure Lines

A Survey on Nonconvex Regularization-Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning

An improved indoor localization method using smartphone inertial sensors

Robust Sparse Recovery in Impulsive Noise via $\ell _p$ -$\ell _1$ Optimization

Dynamic Magnetometer Calibration and Alignment to Inertial Sensors by Kalman Filtering