Results 1 
9 of
9
Transductive Component Analysis
 Proc. IEEE Int’l Conf. Data Mining
, 2008
"... Precession missile feature extraction using sparse ..."
Abstract

Cited by 14 (5 self)
 Add to MetaCart
(Show Context)
Precession missile feature extraction using sparse
Sparse Compositional Metric Learning
"... We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive formulations for global, multitask and local metric learning. ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive formulations for global, multitask and local metric learning. The resulting algorithms have several advantages over existing methods in the literature: a much smaller number of parameters to be estimated and a principled way to generalize learned metrics to new testing data points. To analyze the approach theoretically, we derive a generalization bound that justifies the sparse combination. Empirically, we evaluate our algorithms on several datasets against stateoftheart metric learning methods. The results are consistent with our theoretical findings and demonstrate the superiority of our approach in terms of classification performance and scalability.
TwoStage Metric Learning
"... In this paper, we present a novel twostage metric learning algorithm. We first map each learning instance to a probability distribution by computing its similarities to a set of fixed anchor points. Then, we define the distance in the input data space as the Fisher information distance on the asso ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
In this paper, we present a novel twostage metric learning algorithm. We first map each learning instance to a probability distribution by computing its similarities to a set of fixed anchor points. Then, we define the distance in the input data space as the Fisher information distance on the associated statistical manifold. This induces in the input data space a new family of distance metric with unique properties. Unlike kernelized metric learning, we do not require the similarity measure to be positive semidefinite. Moreover, it can also be interpreted as a local metric learning algorithm with well defined distance approximation. We evaluate its performance on a number of datasets. It outperforms significantly other metric learning methods and SVM. 1.
Geodesic Exponential Kernels: When Curvature and Linearity Conflict
, 2014
"... We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian mani ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic Laplacian kernel can be generalized while retaining positive definiteness. This implies that geodesic Laplacian kernels can be generalized to some curved spaces, including spheres and hyperbolic spaces. Our theoretical results are verified empirically. 1
Metrics for probabilistic geometry
, 2014
"... We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where t ..."
Abstract
 Add to MetaCart
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where the distribution over mappings is given by a Gaussian process. We treat the corresponding latent variable model as a Riemannian manifold and we use the expectation of the metric under the Gaussian process prior to define interpolating paths and measure distance between latent points. We show how distances that respect the expected metric lead to more appropriate generation of new data.
Local highorder . . .
, 2015
"... The common graph Laplacian regularizer is wellestablished in semisupervised learning and spectral dimensionality reduction. However, as a firstorder regularizer, it can lead to degenerate functions in highdimensional manifolds. The iterated graph Laplacian enables highorder regularization, but ..."
Abstract
 Add to MetaCart
The common graph Laplacian regularizer is wellestablished in semisupervised learning and spectral dimensionality reduction. However, as a firstorder regularizer, it can lead to degenerate functions in highdimensional manifolds. The iterated graph Laplacian enables highorder regularization, but it has a high computational complexity and so cannot be applied to large problems. We introduce a new regularizer which is globally high order and so does not suffer from the degeneracy of the graph Laplacian regularizer, but is also sparse for efficient computation in semisupervised learning applications. We reduce computational complexity by building a local firstorder approximation of the manifold as a surrogate geometry, and construct our highorder regularizer based on local derivative evaluations therein. Experiments on human body shape and pose analysis demonstrate the effectiveness and efficiency of our method.
BoundedDistortion Metric Learning
"... Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and numerical inaccuracy. This paper presents boundeddistortion me ..."
Abstract
 Add to MetaCart
(Show Context)
Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and numerical inaccuracy. This paper presents boundeddistortion metric learning (BDML), a new metric learning framework which amounts to finding an optimal Mahalanobis metric space with a boundeddistortion constraint. An efficient solver based on the multiplicative weights update method is proposed. Moreover, we generalize BDML to pseudometric learning and devise the semidefinite relaxation and a randomized algorithm to approximately solve it. We further provide theoretical analysis to show that distortion is a key ingredient for stability and generalization ability of our BDML algorithm. Extensive experiments on several benchmark datasets yield promising results. 1