^{1,2}

^{1,2}

^{1}

^{2}

In order to overcome the limitation of traditional nonnegative factorization algorithms, the paper presents a generalized discriminant orthogonal non-negative tensor factorization algorithm. At first, the algorithm takes the orthogonal constraint into account to ensure the nonnegativity of the low-dimensional features. Furthermore, the discriminant constraint is imposed on low-dimensional weights to strengthen the discriminant capability of the low-dimensional features. The experiments on facial expression recognition have demonstrated that the algorithm is superior to other non-negative factorization algorithms.

Over the past few years, the nonnegative matrix factorization algorithm (NMF) [

However, NMF and its variants have some drawbacks. First of all, NMF requires that all object images should be vectorized in order to find the non-negative decomposition. This vectorization leads to information loss, since the local structure of the image is lost. Moreover, NMF is not unique [

Based on the above analysis, the paper proposes a generalized discriminant orthogonal non-negative tensor factorization algorithm (GDONTF), which makes full use of the class information and imposes the orthogonal constraint to the objective function. The algorithm not only guarantees the non-negativity of low-dimensional features, but also generalizes discriminant constraints to low-dimension features. The experiments on facial expression recognition indicate that GDONTF achieves better performance than other non-negative factorization algorithms.

Consider an

In which,

Since the basis matrix

Take the derivative of

Set (

Left multiply both side of (

The gradient

Because

We have

Consequently, the update rules of

We have conducted facial expression recognition in order to compare the GDONTF with other algorithms such as NMFOS [

The database used for the facial expression recognition experiments is Jaff facial expression database [

Comparison of the best recognition rates for all tested algorithms.

Algorithms | Recognition rate | Algorithms | Recognition rate |
---|---|---|---|

NMF | 79.19% | NMFOS | 89.06% |

DNMF | 92.06% | FisherNMF | 92.06% |

DNTF | 95.24% | GDONTF | 97.07% |

Some images in the Jaff facial expression database.

Facial expression recognition rate versus dimensionality in Jaff database.

In this paper, a generalized discriminant orthogonal non-negative tensor factorization algorithm is proposed considering the orthogonal constraint and the discriminant constraint. For the algorithm, the non-negativity of the low-dimensional features is preserved due to the orthogonal constraint for either training samples or testing samples. In order to enhance the recognition accuracy, the discriminant is conducted on low-dimensional features instead of the weight coefficient of the basis images. The experiments also validate the performance of the algorithm.

The authors declare that there is no conflict of interests regarding the publication of this paper.