Convex Multiview Fisher Discriminant Analysis
英文摘要：
Section 1.3 was incorrect, and 2.1 will be removed from further submissions. A rewritten version will be posted in the future.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Testing for Homogeneity with Kernel Fisher Discriminant Analysis
We propose to investigate test statistics for testing homogeneity in reproducing kernel Hilbert spaces. Asymptotic null distributions under null hypothesis are derived, and consistency against fixed and local alternatives is assessed. Finally, experimental evidence of the performance of the proposed approach on both artificial data and a speaker verification task is provided.
stat.ML
Bayesian Fisher's Discriminant for Functional Data
Institute of Information Science, Academia Sinica（中央研究院资讯科学研究所）；Institute of Statistics, National Chung-Hsing University（中兴大学统计学研究所）；Institute of Networking and Multimedia, National Taiwan University（台湾大学网路与多媒体研究所）
We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated, and we utilize the smoothness assumptions of functional data as prior probabilities. Existing methods which directly employ the smoothness assumption of functional data can be shown as special cases within this framework given corresponding priors while their estimates of the unknowns are one-step approximations to the proposed MAP estimates. Empirical resul…
cs.LGstat.ML
Fisher and Kernel Fisher Discriminant Analysis: Tutorial
University of Waterloo（滑铁卢大学）
This is a detailed tutorial paper which explains the Fisher discriminant Analysis (FDA) and kernel FDA. We start with projection and reconstruction. Then, one- and multi-dimensional FDA subspaces are covered. Scatters in two- and then multi-classes are explained in FDA. Then, we discuss on the rank of the scatters and the dimensionality of the subspace. A real-life example is also provided for interpreting FDA. Then, possible singularity of the scatter is discussed to introduce robust FDA. PCA and FDA directions are also compared. We also prove that FDA and linear discriminant analysis are equ…
cs.LGstat.ML
Randomized Iterative Algorithms for Fisher Discriminant Analysis
Purdue University（普渡大学）
Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is regularized Fisher discriminant analysis (RFDA). In this paper, we present a simple, iterative, sketching-based algorithm for RFDA that comes with provable accuracy guarantees when compared to the conventional approach. Our analysis builds upon two simple structural results that boil down to randomized matrix multiplication, a fundamental and well-understood …
cs.LGstat.ML
Fisher Discriminant Triplet and Contrastive Losses for Training Siamese Networks
University of Waterloo（滑铁卢大学）；Kimia Lab（Kimia实验室）
Siamese neural network is a very powerful architecture for both feature extraction and metric learning. It usually consists of several networks that share weights. The Siamese concept is topology-agnostic and can use any neural network as its backbone. The two most popular loss functions for training these networks are the triplet and contrastive loss functions. In this paper, we propose two novel loss functions, named Fisher Discriminant Triplet (FDT) and Fisher Discriminant Contrastive (FDC). The former uses anchor-neighbor-distant triplets while the latter utilizes pairs of anchor-neighbor …
cs.CVcs.LGstat.ML
LFD-ProtoNet: Prototypical Network Based on Local Fisher Discriminant Analysis for Few-shot Learning
The University of Tokyo（东京大学）；Riken AIP（理化学研究所先进智能项目中心）
The prototypical network (ProtoNet) is a few-shot learning framework that performs metric learning and classification using the distance to prototype representations of each class. It has attracted a great deal of attention recently since it is simple to implement, highly extensible, and performs well in experiments. However, it only takes into account the mean of the support vectors as prototypes and thus it performs poorly when the support set has high variance. In this paper, we propose to combine ProtoNet with local Fisher discriminant analysis to reduce the local within-class covariance a…
cs.LGstat.ML
更多相关论文收起更多论文
Quantized Fisher Discriminant Analysis
University of Waterloo（滑铁卢大学）
This paper proposes a new subspace learning method, named Quantized Fisher Discriminant Analysis (QFDA), which makes use of both machine learning and information theory. There is a lack of literature for combination of machine learning and information theory and this paper tries to tackle this gap. QFDA finds a subspace which discriminates the uniformly quantized images in the Discrete Cosine Transform (DCT) domain at least as well as discrimination of non-quantized images by Fisher Discriminant Analysis (FDA) while the images have been compressed. This helps the user to throw away the origina…
cs.ITcs.LGeess.IV
Unequal Covariance Awareness for Fisher Discriminant Analysis and Its Variants in Classification
Simula Metropolitan（西姆拉大都会中心）；AISIA Research Lab（AISIA研究实验室）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
Fisher Discriminant Analysis (FDA) is one of the essential tools for feature extraction and classification. In addition, it motivates the development of many improved techniques based on the FDA to adapt to different problems or data types. However, none of these approaches make use of the fact that the assumption of equal covariance matrices in FDA is usually not satisfied in practical situations. Therefore, we propose a novel classification rule for the FDA that accounts for this fact, mitigating the effect of unequal covariance matrices in the FDA. Furthermore, since we only modify the clas…
cs.LGstat.ML
Weighted Fisher Discriminant Analysis in the Input and Feature Spaces
University of Waterloo（滑铁卢大学）
Fisher Discriminant Analysis (FDA) is a subspace learning method which minimizes and maximizes the intra- and inter-class scatters of data, respectively. Although, in FDA, all the pairs of classes are treated the same way, some classes are closer than the others. Weighted FDA assigns weights to the pairs of classes to address this shortcoming of FDA. In this paper, we propose a cosine-weighted FDA as well as an automatically weighted FDA in which weights are found automatically. We also propose a weighted FDA in the feature space to establish a weighted kernel FDA for both existing and newly p…
cs.CVcs.LGstat.ML
Asymptotic Generalization Bound of Fisher's Linear Discriminant Analysis
University of Technology, Sydney（悉尼科技大学）
Fisher's linear discriminant analysis (FLDA) is an important dimension reduction method in statistical pattern recognition. It has been shown that FLDA is asymptotically Bayes optimal under the homoscedastic Gaussian assumption. However, this classical result has the following two major limitations: 1) it holds only for a fixed dimensionality $D$, and thus does not apply when $D$ and the training sample size $N$ are proportionally large; 2) it does not provide a quantitative description on how the generalization ability of FLDA is affected by $D$ and $N$. In this paper, we present an asymptoti…
cs.LGstat.ML
Latent Fisher Discriminant Analysis
SUNY at Buffalo（纽约州立大学布法罗分校）
Linear Discriminant Analysis (LDA) is a well-known method for dimensionality reduction and classification. Previous studies have also extended the binary-class case into multi-classes. However, many applications, such as object detection and keyframe extraction cannot provide consistent instance-label pairs, while LDA requires labels on instance level for training. Thus it cannot be directly applied for semi-supervised classification problem. In this paper, we overcome this limitation and propose a latent variable Fisher discriminant analysis model. We relax the instance-level labeling into ba…
cs.CVcs.LGstat.ML
区间Fisher判别分析与可视化
Interval Fisher's Discriminant Analysis and Visualisation
Dep. of Mathematics, Instituto Superior Técnico, ULisboa, Portugal（数学系，技术高级学院，里斯本大学，葡萄牙）；CEMAT, Instituto Superior Técnico, ULisboa, Portugal（CEMAT，技术高级学院，里斯本大学，葡萄牙）；CAMGSD and Dep. of Mathematics, Instituto Superior Técnico, ULisboa, Portugal（CAMGSD和数学系，技术高级学院，里斯本大学，葡萄牙）
本文提出了一种适用于区间值数据的Fisher判别分析方法，并结合可视化工具提升分类结果的可解释性。
cs.LGmath.STstat.ML
Discriminant analysis based on projection onto generalized difference subspace
University of Tsukuba（筑波大学）；National Institute of Advanced Industrial Science and Technology (AIST)（日本产业技术综合研究所（AIST））；University College London（伦敦大学学院）；Royal Institute of Technology (KTH)（皇家理工学院（KTH））
This paper discusses a new type of discriminant analysis based on the orthogonal projection of data onto a generalized difference subspace (GDS). In our previous work, we have demonstrated that GDS projection works as the quasi-orthogonalization of class subspaces, which is an effective feature extraction for subspace based classifiers. Interestingly, GDS projection also works as a discriminant feature extraction through a similar mechanism to the Fisher discriminant analysis (FDA). A direct proof of the connection between GDS projection and FDA is difficult due to the significant difference i…
cs.CVcs.LGstat.ML
基于 Fisher 线性判别（FLD）的近似最优域适应
Approximately optimal domain adaptation with Fisher's Linear Discriminant
Microsoft Research（微软研究院）；Johns Hopkins University（约翰斯·霍普金斯大学）
本文提出基于 FLD 的源任务平均假设与目标任务假设凸组合模型，推导 0-1 损失下的最优组合及可计算近似，并在 EEG、ECG 分类中验证其有效性。
cs.LGeess.SPstat.AP
Sparse Fisher's Linear Discriminant Analysis for Partially Labeled Data
Classification is an important tool with many useful applications. Among the many classification methods, Fisher's Linear Discriminant Analysis (LDA) is a traditional model-based approach which makes use of the covariance information. However, in the high-dimensional, low-sample size setting, LDA cannot be directly deployed because the sample covariance is not invertible. While there are modern methods designed to deal with high-dimensional data, they may not fully use the covariance information as LDA does. Hence in some situations, it is still desirable to use a model-based method such as LD…
stat.MEstat.ML
正交多标签Fisher判别器的谱结构与目标等价性
On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants
本文理论分析了带Stiefel正交约束的多标签线性判别分析，揭示了判别维度可超经典单标签上界，证明了四种Fisher目标在特定约束下等价，并给出了子空间估计误差的近似最优界。
cs.AIcs.LGstat.ML
Supervised Classification Using Sparse Fisher's LDA
It is well known that in a supervised classification setting when the number of features is smaller than the number of observations, Fisher's linear discriminant rule is asymptotically Bayes. However, there are numerous modern applications where classification is needed in the high-dimensional setting. Naive implementation of Fisher's rule in this case fails to provide good results because the sample covariance matrix is singular. Moreover, by constructing a classifier that relies on all features the interpretation of the results is challenging. Our goal is to provide robust classification tha…
stat.COstat.ML
Spectral, Probabilistic, and Deep Metric Learning: Tutorial and Survey
University of Waterloo（滑铁卢大学）
This is a tutorial and survey paper on metric learning. Algorithms are divided into spectral, probabilistic, and deep metric learning. We first start with the definition of distance metric, Mahalanobis distance, and generalized Mahalanobis distance. In spectral methods, we start with methods using scatters of data, including the first spectral metric learning, relevant methods to Fisher discriminant analysis, Relevant Component Analysis (RCA), Discriminant Component Analysis (DCA), and the Fisher-HSIC method. Then, large-margin metric learning, imbalanced metric learning, locally linear metric…
cs.CVcs.LGstat.ML
A ROAD to Classification in High Dimensional Space
For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to circumvent the diverse spectra, and sparse independence rules to mitigate the issue of noise accumulation. However, in biological applications, there are often a group of correlated genes responsible for clinical outcomes, and the use of the covariance information can significantly reduce misclassification rates. The extent of such error rate reductions is unveiled …
stat.MEstat.ML
A Method Based on Convex Cone Model for Image-Set Classification with CNN Features
University of Tsukuba（筑波大学）
In this paper, we propose a method for image-set classification based on convex cone models, focusing on the effectiveness of convolutional neural network (CNN) features as inputs. CNN features have non-negative values when using the rectified linear unit as an activation function. This naturally leads us to model a set of CNN features by a convex cone and measure the geometric similarity of convex cones for classification. To establish this framework, we sequentially define multiple angles between two convex cones by repeating the alternating least squares method and then define the geometric…
cs.CVstat.ML
