Related papers: On Approximating the Lp Distances for p>2

Recently, $l_{2,1}$ matrix norm has been widely applied to many areas such as computer vision, pattern recognition, biological study and etc. As an extension of $l_1$ vector norm, the mixed $l_{2,1}$ matrix norm is often used to find…

Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data. For…

Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two…

Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…

Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…

Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…

We propose a new method for estimating the intrinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We propose a regularization scheme which is motivated by…

Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…

We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…

We study the problem of similarity learning and its application to image retrieval with large-scale data. The similarity between pairs of images can be measured by the distances between their high dimensional representations, and the…

We consider the problem of computing the q->p norm of a matrix A, which is defined for p,q \ge 1, as |A|_{q->p} = max_{x !=0 } |Ax|_p / |x|_q. This is in general a non-convex optimization problem, and is a natural generalization of the…

Despite the remarkable progress facilitated by learning-based stereo-matching algorithms, disparity estimation in low-texture, occluded, and bordered regions still remains a bottleneck that limits the performance. To tackle these…

Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…

Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to…

The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…

We present a heuristic strategy for marginal MAP (MMAP) queries in graphical models. The algorithm is based on a reduction of the task to a polynomial number of marginal inference computations. Given an input evidence, the marginals mass…

Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…

The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired…

Distributed sparse learning with a cluster of multiple machines has attracted much attention in machine learning, especially for large-scale applications with high-dimensional data. One popular way to implement sparse learning is to use…

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…