Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence
The CMU Pose, Illumination, and Expression Database
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Sparse Image Coding Using a 3D Non-Negative Tensor Factorization
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Non-negative tensor factorization with applications to statistics and computer vision
ICML '05 Proceedings of the 22nd international conference on Machine learning
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Cognitive Neuroscience
Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex and Semi-Nonnegative Matrix Factorizations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-negative matrix factorization on Kernels
PRICAI'06 Proceedings of the 9th Pacific Rim international conference on Artificial intelligence
Projective nonnegative matrix factorization for image compression and feature extraction
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
IEEE Transactions on Information Forensics and Security - Part 2
On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization
IEEE Transactions on Neural Networks
Pattern Recognition Letters
Image label completion by pursuing contextual decomposability
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)
Extracting non-negative basis images using pixel dispersion penalty
Pattern Recognition
Measuring the degree of face familiarity based on extended NMF
ACM Transactions on Applied Perception (TAP)
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We present in this paper a general formulation for nonnegative data factorization, called projective nonnegative graph embedding (PNGE), which 1) explicitly decomposes the data into two nonnegative components favoring the characteristics encoded by the so-called intrinsic and penalty graphs [31], respectively, and 2) explicitly describes how to transform each new testing sample into its low-dimensional nonnegative representation. In the past, such a nonnegative decomposition was often obtained for the training samples only, e.g., nonnegative matrix factorization (NMF) and its variants, nonnegative graph embedding (NGE) and its refined version multiplicative nonnegative graph embedding (MNGE). Those conventional approaches for out-of-sample extension either suffer from the high computational cost or violate the basic nonnegative assumption. In this work, PNGE offers a unified solution to out-of-sample extension problem, and the nonnegative coefficient vector of each datum is assumed to be projected from its original feature representation with a universal nonnegative transformation matrix. A convergency provable multiplicative nonnegative updating rule is then derived to learn the basis matrix and transformation matrix. Extensive experiments compared with the state-of-the-art algorithms on nonnegative data factorization demonstrate the algorithmic properties in convergency, sparsity, and classification power.