#### Filter Results:

- Full text PDF available (46)

#### Publication Year

2003

2017

- This year (2)
- Last 5 years (24)
- Last 10 years (46)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Data Set Used

#### Key Phrases

Learn More

- Zhirong Yang, Erkki Oja
- IEEE Transactions on Neural Networks
- 2010

A variant of nonnegative matrix factorization (NMF) which was proposed earlier is analyzed here. It is called projective nonnegative matrix factorization (PNMF). The new method approximately factorizes a projection matrix, minimizing the reconstruction error, into a positive low-rank matrix and its transpose. The dissimilarity between the original data… (More)

- Zhirong Yang, Tele Hao, Onur Dikmen, Xi Chen, Erkki Oja
- NIPS
- 2012

Nonnegative Matrix Factorization (NMF) is a promising relaxation technique for clustering analysis. However, conventional NMF methods that directly approximate the pairwise similarities using the least square error often yield mediocre performance for data in curved manifolds because they can capture only the immediate similarities between data samples.… (More)

- Zhirong Yang, Jorma Laaksonen
- Neurocomputing
- 2007

We present here how to construct multiplicative update rules for non-negative projections based on Oja’s iterative learning rule. Our method integrates the multiplicative normalization factor into the original additive update rule as an additional term which generally has a roughly opposite direction. As a consequence, the modified additive learning rule… (More)

- Zhirong Yang, Zhijian Yuan, Jorma Laaksonen
- IJPRAI
- 2007

We propose a new variant of Non-negative Matrix Factorization (NMF), including its model and two optimization rules. Our method is based on positively constrained projections and is related to the conventional SVD or PCA decomposition. The new model can potentially be applied to image compression and feature extraction problems. Of the latter, we consider… (More)

- Zhirong Yang, Jaakko Peltonen, Samuel Kaski
- ICML
- 2013

Neighbor embedding (NE) methods have found their use in data visualization but are limited in big data analysis tasks due to their O(n) complexity for n data samples. We demonstrate that the obvious approach of subsampling produces inferior results and propose a generic approximated optimization technique that reduces the NE optimization cost to O(n log n).… (More)

- Zhirong Yang, Erkki Oja
- Pattern Recognition
- 2012

In Nonnegative Matrix Factorization (NMF), a nonnegative matrix is approximated by a product of lower-rank factorizing matrices. Most NMF methods assume that each factorizing matrix appears only once in the approximation, thus the approximation is linear in the factorizing matrices. We present a new class of approximative NMF methods, called Quadratic… (More)

- Zhirong Yang, Erkki Oja
- ICML
- 2012

1 Data Sources • Amazon abbreviates the AmazonBinary dataset in Chen’s collection. • Iris is from the UCI machine learning repository . • Votes is from the UCI machine learning repository . • ORL is from the Database of Faces of AT&T. • PIE is from CMU/VASC Image Database. • YaleB is from the Extended Yale Face Database B. • COIL20 is from Columbia… (More)

- Zhirong Yang, Erkki Oja
- IEEE Transactions on Neural Networks
- 2011

Multiplicative updates have been widely used in approximative nonnegative matrix factorization (NMF) optimization because they are convenient to deploy. Their convergence proof is usually based on the minimization of an auxiliary upper-bounding function, the construction of which however remains specific and only available for limited types of dissimilarity… (More)

- Zhirong Yang, Irwin King, Zenglin Xu, Erkki Oja
- NIPS
- 2009

Stochastic Neighbor Embedding (SNE) has shown to be quite promising for data visualization. Currently, the most popular implementation, t-SNE, is restricted to a particular Student t-distribution as its embedding distribution. Moreover, it uses a gradient descent algorithm that may require users to tune parameters such as the learning step size, momentum,… (More)

- Zhirong Yang, Jaakko Peltonen, Samuel Kaski
- ICML
- 2014

Visualization methods that arrange data objects in 2D or 3D layouts have followed two main schools, methods oriented for graph layout and methods oriented for vectorial embedding. We show the two previously separate approaches are tied by an optimization equivalence, making it possible to relate methods from the two approaches and to build new methods that… (More)