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229
Gaussian process latent variable models for visualisation of high dimensional data
 Adv. in Neural Inf. Proc. Sys
, 2004
"... We introduce a variational inference framework for training the Gaussian process latent variable model and thus performing Bayesian nonlinear dimensionality reduction. This method allows us to variationally integrate out the input variables of the Gaussian process and compute a lower bound on the ex ..."
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Cited by 230 (13 self)
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We introduce a variational inference framework for training the Gaussian process latent variable model and thus performing Bayesian nonlinear dimensionality reduction. This method allows us to variationally integrate out the input variables of the Gaussian process and compute a lower bound on the exact marginal likelihood of the nonlinear latent variable model. The maximization of the variational lower bound provides a Bayesian training procedure that is robust to overfitting and can automatically select the dimensionality of the nonlinear latent space. We demonstrate our method on real world datasets. The focus in this paper is on dimensionality reduction problems, but the methodology is more general. For example, our algorithm is immediately applicable for training Gaussian process models in the presence of missing or uncertain inputs. 1
Peopletrackingbydetection and peopledetectionbytracking
 In CVPR’08
"... Both detection and tracking people are challenging problems, especially in complex real world scenes that commonly involve multiple people, complicated occlusions, and cluttered or even moving backgrounds. People detectors have been shown to be able to locate pedestrians even in complex street scene ..."
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Cited by 190 (12 self)
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Both detection and tracking people are challenging problems, especially in complex real world scenes that commonly involve multiple people, complicated occlusions, and cluttered or even moving backgrounds. People detectors have been shown to be able to locate pedestrians even in complex street scenes, but false positives have remained frequent. The identification of particular individuals has remained challenging as well. On the other hand, tracking methods are able to find a particular individual in image sequences, but are severely challenged by realworld scenarios such as crowded street scenes. In this paper, we combine the advantages of both detection and tracking in a single framework. The approximate articulation of each person is detected in every frame based on local features that model the appearance of individual body parts. Prior knowledge on possible articulations and temporal coherency within a walking cycle are modeled using a hierarchical Gaussian process latent variable model (hGPLVM). We show how the combination of these results improves hypotheses for position and articulation of each person in several subsequent frames. We present experimental results that demonstrate how this allows to detect and track multiple people in cluttered scenes with reoccurring occlusions. 1.
Gaussian process dynamical models for human motion
 IEEE TRANS. PATTERN ANAL. MACHINE INTELL
, 2008
"... We introduce Gaussian process dynamical models (GPDMs) for nonlinear time series analysis, with applications to learning models of human pose and motion from highdimensional motion capture data. A GPDM is a latent variable model. It comprises a lowdimensional latent space with associated dynamics, ..."
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Cited by 158 (5 self)
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We introduce Gaussian process dynamical models (GPDMs) for nonlinear time series analysis, with applications to learning models of human pose and motion from highdimensional motion capture data. A GPDM is a latent variable model. It comprises a lowdimensional latent space with associated dynamics, as well as a map from the latent space to an observation space. We marginalize out the model parameters in closed form by using Gaussian process priors for both the dynamical and the observation mappings. This results in a nonparametric model for dynamical systems that accounts for uncertainty in the model. We demonstrate the approach and compare four learning algorithms on human motion capture data, in which each pose is 50dimensional. Despite the use of small data sets, the GPDM learns an effective representation of the nonlinear dynamics in these spaces.
Nonlinear Matrix Factorization with Gaussian Processes
"... A popular approach to collaborative filtering is matrix factorization. In this paper we develop a nonlinear probabilistic matrix factorization using Gaussian process latent variable models. We use stochastic gradient descent (SGD) to optimize the model. SGD allows us to apply Gaussian processes to ..."
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Cited by 74 (1 self)
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A popular approach to collaborative filtering is matrix factorization. In this paper we develop a nonlinear probabilistic matrix factorization using Gaussian process latent variable models. We use stochastic gradient descent (SGD) to optimize the model. SGD allows us to apply Gaussian processes to data sets with millions of observations without approximate methods. We apply our approach to benchmark movie recommender data sets. The results show better than previous stateoftheart performance. 1.
WiFiSLAM Using Gaussian Process Latent Variable Models
 In Proceedings of IJCAI 2007
, 2007
"... WiFi localization, the task of determining the physical location of a mobile device from wireless signal strengths, has been shown to be an accurate method of indoor and outdoor localization and a powerful building block for locationaware applications. However, most localization techniques require ..."
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Cited by 72 (6 self)
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WiFi localization, the task of determining the physical location of a mobile device from wireless signal strengths, has been shown to be an accurate method of indoor and outdoor localization and a powerful building block for locationaware applications. However, most localization techniques require a training set of signal strength readings labeled against a ground truth location map, which is prohibitive to collect and maintain as maps grow large. In this paper we propose a novel technique for solving the WiFi SLAM problem using the Gaussian Process Latent Variable Model (GPLVM) to determine the latentspace locations of unlabeled signal strength data. We show how GPLVM, in combination with an appropriate motion dynamics model, can be used to reconstruct a topological connectivity graph from a signal strength sequence which, in combination with the learned Gaussian Process signal strength model, can be used to perform efficient localization. 1
Local distance preservation in the gplvm through back constraints
 In ICML
, 2006
"... The Gaussian process latent variable model (GPLVM) is a generative approach to nonlinear low dimensional embedding, that provides a smooth probabilistic mapping from latent to data space. It is also a nonlinear generalization of probabilistic PCA (PPCA) (Tipping & Bishop, 1999). While most app ..."
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Cited by 66 (6 self)
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The Gaussian process latent variable model (GPLVM) is a generative approach to nonlinear low dimensional embedding, that provides a smooth probabilistic mapping from latent to data space. It is also a nonlinear generalization of probabilistic PCA (PPCA) (Tipping & Bishop, 1999). While most approaches to nonlinear dimensionality methods focus on preserving local distances in data space, the GPLVM focusses on exactly the opposite. Being a smooth mapping from latent to data space, it focusses on keeping things apart in latent space that are far apart in data space. In this paper we first provide an overview of dimensionality reduction techniques, placing the emphasis on the kind of distance relation preserved. We then show how the GPLVM can be generalized, through back constraints, to additionally preserve local distances. We give illustrative experiments on common data sets. 1.
Gaussian Process Latent Variable Models for Human Pose Estimation
"... We describe a generative approach to recover 3D human pose from image silhouettes. Our method is based on learning a shared low dimensional latent representation capable of generating both human pose and image observations through the GPLVM [1]. We learn a dynamical model over the latent space whic ..."
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Cited by 52 (9 self)
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We describe a generative approach to recover 3D human pose from image silhouettes. Our method is based on learning a shared low dimensional latent representation capable of generating both human pose and image observations through the GPLVM [1]. We learn a dynamical model over the latent space which allows us to disambiguate between ambiguous silhouettes by temporal consistency. The model has only two free parameters and requires no manual initialization. 1.
Gaussianprocess factor analysis for lowdimensional singletrial analysis of neural population activity
 J Neurophysiol
"... You might find this additional information useful... A corrigendum for this article has been published. It can be found at: ..."
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Cited by 52 (15 self)
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You might find this additional information useful... A corrigendum for this article has been published. It can be found at:
Dimensionality Reduction: A Comparative Review
, 2008
"... In recent years, a variety of nonlinear dimensionality reduction techniques have been proposed, many of which rely on the evaluation of local properties of the data. The paper presents a review and systematic comparison of these techniques. The performances of the techniques are investigated on arti ..."
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Cited by 42 (0 self)
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In recent years, a variety of nonlinear dimensionality reduction techniques have been proposed, many of which rely on the evaluation of local properties of the data. The paper presents a review and systematic comparison of these techniques. The performances of the techniques are investigated on artificial and natural tasks. The results of the experiments reveal that nonlinear techniques perform well on selected artificial tasks, but do not outperform the traditional PCA on realworld tasks. The paper explains these results by identifying weaknesses of current nonlinear techniques, and suggests how the performance of nonlinear dimensionality reduction techniques may be improved.
Articulated pose estimation in a learned smooth space of feasible solutions
 IN: WORSHOP ON LEARNING IN COMPUTER VISION AND PATTERN RECOGNITION
, 2005
"... A learning based framework is proposed for estimating human body pose from a single image. Given a differentiable function that maps from pose space to image feature space, the goal is to invert the process: estimate the pose given only image features. The inversion is an illposed problem as the in ..."
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Cited by 40 (3 self)
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A learning based framework is proposed for estimating human body pose from a single image. Given a differentiable function that maps from pose space to image feature space, the goal is to invert the process: estimate the pose given only image features. The inversion is an illposed problem as the inverse mapping is a one to many process, hence multiple solutions exist. It is desirable to restrict the solution space to a smaller subset of feasible solutions. The space of feasible solutions may not admit a closed form description. The proposed framework seeks to learn an approximation over such a space. Using Gaussian Process Latent Variable Modelling. The scaled conjugate gradient method is used to find the best matching pose in the learned space. The formulation allows easy incorporation of various constraints for more accurate pose estimation. The performance of the proposed approach is evaluated in the task of upperbody pose estimation from silhouettes and compared with the Specialized Mapping Architecture. The proposed approach performs better than the latter approach in terms of estimation accuracy with synthetic data and qualitatively better results with real video of humans performing gestures.