Related papers: Multiple Closed-Form Local Metric Learning for K-N…
For many machine learning algorithms such as $k$-Nearest Neighbor ($k$-NN) classifiers and $ k $-means clustering, often their success heavily depends on the metric used to calculate distances between different data points. An effective…
Distance metric learning is a successful way to enhance the performance of the nearest neighbor classifier. In most cases, however, the distribution of data does not obey a regular form and may change in different parts of the feature…
We consider the supervised classification problem of machine learning in Cayley-Klein projective geometries: We show how to learn a curved Mahalanobis metric distance corresponding to either the hyperbolic geometry or the elliptic geometry…
Metric learning is an important family of algorithms for classification and similarity search, but the robustness of learned metrics against small adversarial perturbations is less studied. In this paper, we show that existing metric…
The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This…
Metric learning aims at finding a suitable distance metric over the input space, to improve the performance of distance-based learning algorithms. In high-dimensional settings, it can also serve as dimensionality reduction by imposing a…
Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the…
We propose to learn multiple local Mahalanobis distance metrics to perform k-nearest neighbor (kNN) classification of temporal sequences. Temporal sequences are first aligned by dynamic time warping (DTW); given the alignment path,…
We propose a new method for local distance metric learning based on sample similarity as side information. These local metrics, which utilize conical combinations of metric weight matrices, are learned from the pooled spatial…
The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN performance. In this paper, we study the…
Clustering and classification critically rely on distance metrics that provide meaningful comparisons between data points. We present mixed-integer optimization approaches to find optimal distance metrics that generalize the Mahalanobis…
A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric.…
Naive Bayes Nearest Neighbour (NBNN) is a simple and effective framework which addresses many of the pitfalls of K-Nearest Neighbour (KNN) classification. It has yielded competitive results on several computer vision benchmarks. Its central…
In recent years, the crucial importance of metrics in machine learning algorithms has led to an increasing interest for optimizing distance and similarity functions. Most of the state of the art focus on learning Mahalanobis distances…
The k Nearest Neighbors (kNN) method has received much attention in the past decades, where some theoretical bounds on its performance were identified and where practical optimizations were proposed for making it work fairly well in high…
$K$-NN classifier is one of the most famous classification algorithms, whose performance is crucially dependent on the distance metric. When we consider the distance metric as a parameter of $K$-NN, learning an appropriate distance metric…
Large margin nearest neighbor (LMNN) is a metric learner which optimizes the performance of the popular $k$NN classifier. However, its resulting metric relies on pre-selected target neighbors. In this paper, we address the feasibility of…
Metric learning methods for dimensionality reduction in combination with k-Nearest Neighbors (kNN) have been extensively deployed in many classification, data embedding, and information retrieval applications. However, most of these…
This report provides an exploration of different distance measures that can be used with the $K$-means algorithm for cluster analysis. Specifically, we investigate the Mahalanobis distance, and critically assess any benefits it may have…
In this paper, we propose to learn a Mahalanobis distance to perform alignment of multivariate time series. The learning examples for this task are time series for which the true alignment is known. We cast the alignment problem as a…