Trace Ratio vs. Ratio Trace for Dimensionality Reduction

By Huan Wang, Shuicheng Yan, Dong Xu, Xiaoou Tang, Thomas S. Huang. 2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007

378 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/a07869140df589bea88695309f89cf9160d8a664

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Yi Yang
2. Jiliang Tang
3. Shuicheng Yan
4. Jiebo Luo
5. Huan Liu
6. Lei Zhang
7. Feiping Nie
8. Dacheng Tao

In Computational Mechanics

1. Lei Zhang
2. David Dapeng Zhang
3. Xiangchu Feng
4. Meng Yang
5. Feiping Nie
6. Jie Chen
7. Effrosini Kokiopoulou
8. Y. Saad

In Computer Vision and Pattern Recognition

1. Yi Yang
2. Dacheng Tao
3. Lei Zhang
4. Luc Van Gool
5. Ming-Hsuan Yang
6. Xiaogang Wang
7. Shuicheng Yan
8. Trevor Darrell

Citations in the corpus

• Motor Bearing Fault Diagnosis Using Trace Ratio Linear Discriminant Analysis (2014, methodology): “When evaluating the similarities between data points based on Euclidean distance, the orthogonal projection can preserve such similarities without any change [37].”
• Trace optimization and eigenproblems in dimension reduction methods (2011, background): “In [49] and [19] algorithms were proposed to solve (2.3) by computing this root and by exploiting the above relations.”
• Learning a Mahalanobis distance metric for data clustering and classification (2008, methodology): “Mathematically, our formulation about the problem by maximizing the ratio of distances yields just the same form of objective function used in literature [60] [65] [66].”
• Sparse Representation Based Fisher Discrimination Dictionary Learning for Image Classification (2014, methodology): “The Fisher criterion has been widely used in subspace learning (Wang et al. 2007) to learn a discriminative subspace, and it is usually defined as to minimize the trace ratio tr(SW (X))/tr(SB(X)), where tr(•) means the trace of a matrix.”
• Trace Ratio Criterion for Feature Selection (2008, background): “These feature selection algorithms can also be categorized into wrappers and filters (Kohavi & John 1997; Das 2001).”
• Feature Selection (2016, methodology): “ave a closed-form solution. Hence, the trace ratio problem is often converted into a more tractable format called the ratio trace problem by maximizing tr[(W′X′LwXW)−1(W′X′LbXW)]. As an alternative, [Wang et al. 2007] propose an iterative algorithm called ITR to solve the trace ratio problem directl”
• A Multimedia Retrieval Framework Based on Semi-Supervised Ranking and Relevance Feedback (2012, positive): “The recent work [31] has experimentally demonstrated that better performances can be achieved in pattern recognition if we solve the original trace ratio optimization problem shown in (36) as opposed to the ratio trace problem shown in (37).”