# Learning the parts of objects by non-negative matrix factorization

@article{Lee1999LearningTP, title={Learning the parts of objects by non-negative matrix factorization}, author={Daniel D. Lee and H. Sebastian Seung}, journal={Nature}, year={1999}, volume={401}, pages={788-791} }

Is perception of the whole based on perception of its parts. [... ] Key Method Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. When non-negative matrix factorization is implemented as a neural network, parts-based representations emerge by virtue of two properties: the firing rates of neurons are never negative and synaptic… Expand

## 11,332 Citations

Learning the parts of objects by auto-association

- Computer ScienceNeural Networks
- 2002

Local non-negative matrix factorization as a visual representation

- Computer ScienceProceedings 2nd International Conference on Development and Learning. ICDL 2002
- 2002

A set of orthogonal, binary, localized basis components are learned from a well-aligned face image database and leads to a Walsh function-based representation of the face images, which can be used to resolve the occlusion problem, improve the computing efficiency and compress the storage requirements of a face detection and recognition system.

A modular non-negative matrix factorization for parts-based object recognition using subspace representation

- Computer ScienceElectronic Imaging
- 2008

A novel modular NMF algorithm is developed which provides uniquely separated basis vectors which code individual face parts in accordance with the parts-based principle of the NMF methodology applied to object recognition problems, but any significant improvement of recognition rates for occluded parts was not reached.

Face recognition using localized features based on non-negative sparse coding

- Computer ScienceMachine Vision and Applications
- 2006

Non-Negative Sparse Coding applied to the learning of facial features for face recognition was found to be the best approach of the three part-based methods, although it must be observed that the best distance measure was not consistent for the different experiments.

A-Optimal Non-negative Projection for image representation

- Computer Science2012 IEEE Conference on Computer Vision and Pattern Recognition
- 2012

This paper proposes a novel method, called A-Optimal Non-negative Projection (ANP), which imposes a constraint on the encoding factor as a regularizer during matrix factorization to preserve more intrinsic characteristics of the data regardless of any specific labels.

Learning Parts-based Representations with Nonnegative Restricted Boltzmann Machine

- Computer ScienceACML
- 2013

The capacity of RBMs is enhanced by introducing nonnegativity into the model weights, resulting in a variant called nonnegative restricted Boltzmann machine (NRBM), which produces not only controllable decomposition of data into interpretable parts but also a way to estimate the intrinsic nonlinear dimensionality of data.

Topographic NMF for Data Representation

- Computer ScienceIEEE Transactions on Cybernetics
- 2014

A topographic NMF (TNMF), which imposes a topographic constraint on the encoding factor as a regularizer during matrix factorization, and which will force the encodings to be organized in a topographical map so that the feature invariance can be promoted.

Non-Negative Matrix Factorization with Constraints

- Computer ScienceAAAI
- 2010

This paper proposes a novel semi-supervised matrix decomposition method, called Constrained Non-negative Matrix Factorization, which takes the label information as additional constraints and requires that the data points sharing the same label have the same coordinate in the new representation space.

Leveraging maximum entropy and correlation on latent factors for learning representations

- Computer ScienceNeural Networks
- 2020

Projective Nonnegative Matrix Factorization : Sparseness , Orthogonality , and Clustering

- Computer Science
- 2009

It is shown that PNMF is intimately related to ”soft” k-means clustering and is able to outperform NMF in document classification tasks and derives bases which are somewhat better for a localized representation than NMF, more orthogonal, and produce considerably more sparse representations.

## References

SHOWING 1-10 OF 47 REFERENCES

Independent component representations for face recognition

- Computer ScienceElectronic Imaging
- 1998

ICA was performed on a set of face images by an unsupervised learning algorithm derived from the principle of optimal information transfer through sigmoidal neurons, which maximizes the mutual information between the input and the output, which produces statistically independent outputs under certain conditions.

Recognition-by-components: a theory of human image understanding.

- Computer SciencePsychological review
- 1987

Recognition-by-components (RBC) provides a principled account of the heretofore undecided relation between the classic principles of perceptual organization and pattern recognition.

Eigenfaces for Recognition

- Computer ScienceJournal of Cognitive Neuroscience
- 1991

A near-real-time computer system that can locate and track a subject's head, and then recognize the person by comparing characteristics of the face to those of known individuals, and that is easy to implement using a neural network architecture.

Emergence of simple-cell receptive field properties by learning a sparse code for natural images

- Computer ScienceNature
- 1996

It is shown that a learning algorithm that attempts to find sparse linear codes for natural scenes will develop a complete family of localized, oriented, bandpass receptive fields, similar to those found in the primary visual cortex.

High-Level Vision: Object Recognition and Visual Cognition

- Computer Science
- 1996

Object recognition: shape-based recognition what is recognition? why object recognition is difficult. Approaches to object recognition: invariant properties and feature spaces parts and structural…

What Is the Goal of Sensory Coding?

- Computer ScienceNeural Computation
- 1994

It is proposed that compact coding schemes are insufficient to account for the receptive field properties of cells in the mammalian visual pathway and suggested that natural scenes, to a first approximation, can be considered as a sum of self-similar local functions (the inverse of a wavelet).

An Information-Maximization Approach to Blind Separation and Blind Deconvolution

- Computer ScienceNeural Computation
- 1995

It is suggested that information maximization provides a unifying framework for problems in "blind" signal processing and dependencies of information transfer on time delays are derived.

Visual object recognition.

- Psychology, BiologyAnnual review of neuroscience
- 1996

Evidence from psychology, neuropsychology, and neurophysiology supports the idea that there are multiple systems for recognition of objects, and indicates that one system may represent objects by combinations of multiple views, or aspects, and another may representObjects by structural primitives and their spatial interrelationships.