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Orthogonal NMF through Subspace Exploration

Megasthenis Asteris, Dimitris S. Papailiopoulos, Alexandros G. Dimakis
2015 Neural Information Processing Systems  
Orthogonal Nonnegative Matrix Factorization (ONMF) aims to approximate a nonnegative matrix as the product of two k-dimensional nonnegative factors, one of which has orthonormal columns.  ...  Orthogonal NMF (ONMF) [9] is a variant of NMF with an additional orthogonality constraint: given a real nonnegative m × n matrix M and a target dimension k, typically much smaller than m and n, we seek  ...  Introduction Orthogonal NMF The success of Nonnegative Matrix Factorization (NMF) in a range of disciplines spanning data mining, chemometrics, signal processing and more, has driven an extensive practical  ... 
dblp:conf/nips/AsterisPD15 fatcat:dmajn2luirdhdmak5d4ochgove

Nonnegative Matrix Factorizations Performing Object Detection and Localization

G. Casalino, N. Del Buono, M. Minervini
2012 Applied Computational Intelligence and Soft Computing  
Nonnegative matrix factorization represents an emerging example of subspace methods, which is able to extract interpretable parts from a set of template image objects and then to additively use them for  ...  The problem to be explored here can be formalized as follows.  ...  Differently to other subspace methods, the learned basis vectors in NMF are not orthonormal to each other.  ... 
doi:10.1155/2012/781987 fatcat:tagln6nujzdx5au4xw3iobty7i

Intersecting Faces: Non-negative Matrix Factorization With New Guarantees [article]

Rong Ge, James Zou
2015 arXiv   pre-print
We explored the performance of Face-Intersect on simulations and discuss settings where it empirically outperformed the state-of-art methods.  ...  Recently a surge of research have focused on a very restricted class of NMFs, called separable NMF, where provably correct algorithms have been developed.  ...  Let B be the projection of W to the orthogonal subspace of Q, and remove the 0-columns in B.  ... 
arXiv:1507.02189v1 fatcat:m7izss5kifconegjjtl45lnnkm

Nonnegative Discriminant Matrix Factorization

Yuwu Lu, Zhihui Lai, Yong Xu, Xuelong Li, David Zhang, Chun Yuan
2017 IEEE transactions on circuits and systems for video technology (Print)  
NDMF projects the low-dimensional representation of the subspace of the base matrix to regularize the NMF for discriminant subspace learning.  ...  NDMF integrates the nonnegative constraint, orthogonality and discriminant information in the objective function.  ...  of NMF to obtain the discriminant subspace [19] , [20] .  ... 
doi:10.1109/tcsvt.2016.2539779 fatcat:cdvoyrgk4nh3nlf5ezz5zdtdke

Categorical Dimensions of Human Odor Descriptor Space Revealed by Non-Negative Matrix Factorization

Jason B. Castro, Arvind Ramanathan, Chakra S. Chennubhotla, Andreas Schaefer
2013 PLoS ONE  
The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space.  ...  Here, we use nonnegative matrix factorization (NMF) -a dimensionality reduction technique -to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor  ...  To explore this potential fine-scale structure wherein subsets of odorants show distinct correlations among subsets of descriptors, we sought submatrices of WH (the NMF approximation to the original data  ... 
doi:10.1371/journal.pone.0073289 pmid:24058466 pmcid:PMC3776812 fatcat:zazmlsxqjbfgnnygxbxqdob7um

Nested Nonnegative Cone Analysis [article]

Lingsong Zhang and J. S. Marron and Shu Lu
2013 arXiv   pre-print
The nonnegative matrix factorization (NMF) approach overcomes this issue, however the NMF approximation matrices suffer several drawbacks: 1) the factorization may not be unique, 2) the resulting approximation  ...  matrix at a specific rank may not be unique, and 3) the subspaces spanned by the approximation matrices at different ranks may not be nested.  ...  The SVD rank 2 and 1 approximating cones are the intersections of subspaces, a plane and a line through the origin, with the octant (top left panel).  ... 
arXiv:1308.4206v2 fatcat:jldznwdmvzhnbdhzdwuzsinqn4

Age estimation based on extended non-negative matrix factorization

Ce Zhan, Wanqing Li, Philip Ogunbona
2011 2011 IEEE 13th International Workshop on Multimedia Signal Processing  
To emphasize the appearance variation in aging, one individual extended NMF subspace is learned for each age or age group.  ...  In this paper, non-negative matrix factorization (NMF) is extended to learn a localized non-overlapping subspace representation for age estimation.  ...  Extended NMF In the proposed method, we extend the NMF for producing a localized, non-overlapping subspace representation.  ... 
doi:10.1109/mmsp.2011.6093779 dblp:conf/mmsp/ZhanLO11 fatcat:dj25dhwfnzb77m7q2j674mh37e

Multiple Independent Subspace Clusterings

Xing Wang, Jun Wang, Carlotta Domeniconi, Guoxian Yu, Guoqiang Xiao, Maozu Guo
2019 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
In the second stage, to account for the intrinsic geometric structure of samples embedded in each subspace, MISC performs graph regularized semi-nonnegative matrix factorization to explore clusters.  ...  In the first stage, MISC uses independent subspace analysis to seek multiple and statistical independent (i.e. non-redundant) subspaces, and determines the number of subspaces via the minimum description  ...  COALA (Constrained Orthogonal Average Link Algorithm) (Bae and Bailey 2006) is the classic algorithm that controls redundancy through clustering labels.  ... 
doi:10.1609/aaai.v33i01.33015353 fatcat:iwwpbvfyc5csba3ylrpgyephsi

Multiple Independent Subspace Clusterings [article]

Xing Wang, Jun Wang, Carlotta Domeniconi, Guoxian Yu, Guoqiang Xiao, Maozu Guo
2019 arXiv   pre-print
In the second stage, to account for the intrinsic geometric structure of samples embedded in each subspace, MISC performs graph regularized semi-nonnegative matrix factorization to explore clusters.  ...  In the first stage, MISC uses independent subspace analysis to seek multiple and statistical independent (i.e. non-redundant) subspaces, and determines the number of subspaces via the minimum description  ...  COALA (Constrained Orthogonal Average Link Algorithm) (Bae and Bailey 2006) is the classic algorithm that controls redundancy through clustering labels.  ... 
arXiv:1905.04191v1 fatcat:7zapqjcz2vb7foomc6ppmtp4ye

Subspace Nonnegative Matrix Factorization for Feature Representation [article]

Junhang Li, Jiao Wei, Can Tong, Tingting Shen, Yuchen Liu, Chen Li, Shouliang Qi, Yudong Yao, Yueyang Teng
2022 arXiv   pre-print
This paper proposes a new NMF method by introducing adaptive weights to identify key features in the original space so that only a subspace involves generating the new representation.  ...  Traditional nonnegative matrix factorization (NMF) learns a new feature representation on the whole data space, which means treating all features equally.  ...  We take ConvexNMF [19] as an example to construct two new subspace NMF methods.  ... 
arXiv:2204.08382v1 fatcat:bigdpc3ptbckri4fjiunlrx2ry

CANCER MOLECULAR PATTERN DISCOVERY BY SUBSPACE CONSENSUS KERNEL CLASSIFICATION

Xiaoxu Han
2007 Computational Systems Bioinformatics  
The algorithm is a consensus kernel hierarchical clustering (CKHC) method in the subspace generated by the PG-NMF.  ...  In this work, we describe a subspace consensus kernel clustering algorithm based on the projected gradient nonnegative matrix factorization (PG-NMF).  ...  They also have potentials to explore the latent structure of data.  ... 
doi:10.1142/9781860948732_0010 fatcat:drscwtsesfcm7iudjcfnztqiva

Orthogonal symmetric non-negative matrix factorization under the stochastic block model [article]

Subhadeep Paul, Yuguo Chen
2016 arXiv   pre-print
We establish the connection of the factors obtained through the factorization to a non-negative basis of an invariant subspace of the estimated matrix, drawing parallel with the spectral clustering.  ...  We present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks.  ...  needs to be explored further.  ... 
arXiv:1605.05349v1 fatcat:7vy24yr6avckjigqg3q6mj75w4

Adaptive RGB Image Recognition by Visual-Depth Embedding

Ziyun Cai, Yang Long, Ling Shao
2018 IEEE Transactions on Image Processing  
Through solving this problem, we can make the projection orthogonal: min P P A − V , s.t. P T P = I, (25) where P is the orthogonal projection for target domain.  ...  Then we transfer the knowledge of depth information to the target dataset through an orthogonal projection to align the data in the shared latent feature space with the target domain.  ... 
doi:10.1109/tip.2018.2806839 pmid:29994784 fatcat:7ie5bp6jsrhyvistkv6ftixeyi

Non-Negative Group Sparsity with Subspace Note Modelling for Polyphonic Transcription

Ken O'Hanlon, Hidehisa Nagano, Nicolas Keriven, Mark D. Plumbley
2016 IEEE/ACM Transactions on Audio Speech and Language Processing  
ACKNOWLEDGMENT The authors would like to thank the reviewers for useful comments, and the authors of [50] [4] for making the code for H-NMF freely available, in particular to Roland Badeau for discussions  ...  CONCLUSIONS In this paper the use of group sparsity with subspace modelling for piano transcription was explored.  ...  In particular, the coupling between narrowband atoms is effected through data in H-NMF, while it is effected simply by the group sparse penalty in GS--NMD.  ... 
doi:10.1109/taslp.2016.2515514 fatcat:4yowl4nzlneoxgcsjwylorjvbm

Non-negative matrix factorisation for object class discovery and image auto-annotation

Jiayu Tang, Paul H. Lewis
2008 Proceedings of the 2008 international conference on Content-based image and video retrieval - CIVR '08  
Non-negative matrix factorisation (NMF), which generates a non-negative representation of data through matrix decomposition, is one such technique.  ...  In this paper, we present the novel use of NMF in two tasks; object class detection and automatic annotation of images.  ...  Therefore, the axes of the semantic space that capture the topics are not necessarily orthogonal, which is the case for the subspace generated by SVD.  ... 
doi:10.1145/1386352.1386370 dblp:conf/civr/TangL08 fatcat:hglozvxehje2zaeg5g5umzx4ye
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