Topic
Hinge loss
About: Hinge loss is a research topic. Over the lifetime, 798 publications have been published within this topic receiving 30244 citations.
Papers published on a yearly basis
Papers
TL;DR: This paper shows how to learn a Mahalanobis distance metric for kNN classification from labeled examples in a globally integrated manner and finds that metrics trained in this way lead to significant improvements in kNN Classification.
Abstract: The accuracy of k-nearest neighbor (kNN) classification depends significantly on the metric used to compute distances between different examples. In this paper, we show how to learn a Mahalanobis distance metric for kNN classification from labeled examples. The Mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes kNN classification using Euclidean distances. In our approach, the metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. As in support vector machines (SVMs), the margin criterion leads to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our approach requires no modification or extension for problems in multiway (as opposed to binary) classification. In our framework, the Mahalanobis distance metric is obtained as the solution to a semidefinite program. On several data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification. Sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster. We show how to learn and combine these local metrics in a globally integrated manner.
5,708 citations
Proceedings Article•
5 Dec 2005TL;DR: In this article, a Mahanalobis distance metric for k-NN classification is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin.
Abstract: We show how to learn a Mahanalobis distance metric for k-nearest neighbor (kNN) classification by semidefinite programming. The metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. On seven data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification—for example, achieving a test error rate of 1.3% on the MNIST handwritten digits. As in support vector machines (SVMs), the learning problem reduces to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our framework requires no modification or extension for problems in multiway (as opposed to binary) classification.
4,625 citations
1 Jun 2016
TL;DR: The representation learned by this approach, when combined with a simple k-nearest neighbor (kNN) algorithm, shows significant improvements over existing methods on both high- and low-level vision classification tasks that exhibit imbalanced class distribution.
Abstract: Data in vision domain often exhibit highly-skewed class distribution, i.e., most data belong to a few majority classes, while the minority classes only contain a scarce amount of instances. To mitigate this issue, contemporary classification methods based on deep convolutional neural network (CNN) typically follow classic strategies such as class re-sampling or cost-sensitive training. In this paper, we conduct extensive and systematic experiments to validate the effectiveness of these classic schemes for representation learning on class-imbalanced data. We further demonstrate that more discriminative deep representation can be learned by enforcing a deep network to maintain both intercluster and inter-class margins. This tighter constraint effectively reduces the class imbalance inherent in the local data neighborhood. We show that the margins can be easily deployed in standard deep learning framework through quintuplet instance sampling and the associated triple-header hinge loss. The representation learned by our approach, when combined with a simple k-nearest neighbor (kNN) algorithm, shows significant improvements over existing methods on both high-and low-level vision classification tasks that exhibit imbalanced class distribution.
1,334 citations
TL;DR: A nonasymptotic oracle inequality is proved for the empirical risk minimizer with Lasso penalty for high-dimensional generalized linear models with Lipschitz loss functions, and the penalty is based on the coefficients in the linear predictor, after normalization with the empirical norm.
Abstract: We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear predictor, after normalization with the empirical norm. The examples include logistic regression, density estimation and classification with hinge loss. Least squares regression is also discussed.
918 citations
TL;DR: This paper proves tight data-dependent bounds for the risk of this hypothesis in terms of an easily computable statistic M/sub n/ associated with the on-line performance of the ensemble, and obtains risk tail bounds for kernel perceptron algorithms interms of the spectrum of the empirical kernel matrix.
Abstract: In this paper, it is shown how to extract a hypothesis with small risk from the ensemble of hypotheses generated by an arbitrary on-line learning algorithm run on an independent and identically distributed (i.i.d.) sample of data. Using a simple large deviation argument, we prove tight data-dependent bounds for the risk of this hypothesis in terms of an easily computable statistic M/sub n/ associated with the on-line performance of the ensemble. Via sharp pointwise bounds on M/sub n/, we then obtain risk tail bounds for kernel perceptron algorithms in terms of the spectrum of the empirical kernel matrix. These bounds reveal that the linear hypotheses found via our approach achieve optimal tradeoffs between hinge loss and margin size over the class of all linear functions, an issue that was left open by previous results. A distinctive feature of our approach is that the key tools for our analysis come from the model of prediction of individual sequences; i.e., a model making no probabilistic assumptions on the source generating the data. In fact, these tools turn out to be so powerful that we only need very elementary statistical facts to obtain our final risk bounds.
743 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 6 |
| 2024 | 7 |
| 2023 | 27 |
| 2022 | 65 |
| 2021 | 80 |
| 2020 | 81 |