# Non-negative Matrix Factorization for Self-calibration of Photometric Redshift Scatter in Weak-lensing Surveys

## Abstract

Photo- z error is one of the major sources of systematics degrading the accuracy of weak-lensing cosmological inferences. Zhang et al. proposed a self-calibration method combining galaxy–galaxy correlations and galaxy–shear correlations between different photo- z bins. Fisher matrix analysis shows that it can determine the rate of photo- z outliers at a level of 0.01%–1% merely using photometric data and do not rely on any prior knowledge. In this paper, we develop a new algorithm to implement this method by solving a constrained nonlinear optimization problem arising in the self-calibration process. Based on the techniques of fixed-point iteration and non-negative matrix factorization, the proposed algorithm can efficiently and robustly reconstruct the scattering probabilities between the true- z and photo- z bins. The algorithm has been tested extensively by applying it to mock data from simulated stage IV weak-lensing projects. We find that the algorithm provides a successful recovery of the scatter rates at the level of 0.01%–1%, and the true mean redshifts of photo- z bins at the level of 0.001, which may satisfy the requirements in future lensing surveys.

- Authors:

- Department of Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 (China)

- Publication Date:

- OSTI Identifier:
- 22679765

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 848; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALGORITHMS; CALIBRATION; CORRELATIONS; COSMOLOGY; FACTORIZATION; GALAXIES; GRAVITATIONAL LENSES; NONLINEAR PROBLEMS; OPTIMIZATION; PROBABILITY; RED SHIFT; SCATTERING; SIMULATION

### Citation Formats

```
Zhang, Le, Yu, Yu, and Zhang, Pengjie, E-mail: lezhang@sjtu.edu.cn.
```*Non-negative Matrix Factorization for Self-calibration of Photometric Redshift Scatter in Weak-lensing Surveys*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/AA8C72.

```
Zhang, Le, Yu, Yu, & Zhang, Pengjie, E-mail: lezhang@sjtu.edu.cn.
```*Non-negative Matrix Factorization for Self-calibration of Photometric Redshift Scatter in Weak-lensing Surveys*. United States. doi:10.3847/1538-4357/AA8C72.

```
Zhang, Le, Yu, Yu, and Zhang, Pengjie, E-mail: lezhang@sjtu.edu.cn. Tue .
"Non-negative Matrix Factorization for Self-calibration of Photometric Redshift Scatter in Weak-lensing Surveys". United States. doi:10.3847/1538-4357/AA8C72.
```

```
@article{osti_22679765,
```

title = {Non-negative Matrix Factorization for Self-calibration of Photometric Redshift Scatter in Weak-lensing Surveys},

author = {Zhang, Le and Yu, Yu and Zhang, Pengjie, E-mail: lezhang@sjtu.edu.cn},

abstractNote = {Photo- z error is one of the major sources of systematics degrading the accuracy of weak-lensing cosmological inferences. Zhang et al. proposed a self-calibration method combining galaxy–galaxy correlations and galaxy–shear correlations between different photo- z bins. Fisher matrix analysis shows that it can determine the rate of photo- z outliers at a level of 0.01%–1% merely using photometric data and do not rely on any prior knowledge. In this paper, we develop a new algorithm to implement this method by solving a constrained nonlinear optimization problem arising in the self-calibration process. Based on the techniques of fixed-point iteration and non-negative matrix factorization, the proposed algorithm can efficiently and robustly reconstruct the scattering probabilities between the true- z and photo- z bins. The algorithm has been tested extensively by applying it to mock data from simulated stage IV weak-lensing projects. We find that the algorithm provides a successful recovery of the scatter rates at the level of 0.01%–1%, and the true mean redshifts of photo- z bins at the level of 0.001, which may satisfy the requirements in future lensing surveys.},

doi = {10.3847/1538-4357/AA8C72},

journal = {Astrophysical Journal},

number = 1,

volume = 848,

place = {United States},

year = {Tue Oct 10 00:00:00 EDT 2017},

month = {Tue Oct 10 00:00:00 EDT 2017}

}