**2.2. Multi-orientation weighted symmetric local graph structure (MOW-SLGS)**

MOW-SLGS algorithm [10] is improved based on the LGS algorithm, which mitigates the problems of the LGS algorithm by constructing the graph structure in the horizontal direction. The extracted feature for the target pixel is not sufficient, and the weight ratio is not balanced. The algorithm is implemented as follows: in the 5 × 5 neighborhood, we take the center pixel as the target pixel, and then the graph structure is constructed by the target pixel in 0, 45, 90, and 135° direction. Finally, we calculate the feature values of each direction. For the directions of 0, 45, and 135°, the left side of the target pixel is used to compare the value of the pixel in the counterclockwise direction, the right side of the target pixel to compare the value of the pixel in the clockwise direction. If the pixel value is larger, we set it to 1; otherwise set 0. For the direction of 90°, the comparison of the upper side of the target pixel with counter-clockwise order, the lower side of the target pixel with the counter-clockwise order. The binary value is read from the central pixel along each direction. Each direction is firstly in the counter-clockwise order, and then in the clockwise order. The weight of the 8-bit binary number obtained by the algorithm of MOW-SLGS in each direction is shown in **Figure 2**, where X<sup>0</sup> is the target pixel. Finally, the maximum value is obtained as the characteristic value.

We take the direction of 45° as the example as shown in **Figure 3**. It can be seen that the characteristic value of the target pixel in the direction of 45° is 01101101. Thus, the final value is 122 after calculating its corresponding decimal value.

**Figure 1.** Template of LGS operator and its example.

Thus, extracting the effective facial feature information from the occluded faces is the key

Many feature extraction algorithms have been proposed to extract facial features; the extracted features can be divided into global features [3] and local features [4–6]. It has been shown that the extracted global facial features cannot effectively solve the recognition problems with occluded faces [7]. On the other hand, local features could deal with face recognition with

Abusham et al. [8] proposed the Local Graph Structure (LGS) operator, which combines 5 pixels around the center pixel into a graph structure in the neighborhood of 3 × 4. The LGS algorithm improves the recognition rate through the efficient use of pixel information in the neighborhood. However, the graph structure constructed by the LGS algorithm is unbalanced. Abdullah et al. [9] proposed a Symmetric Local Graph Structure (SLGS) algorithm to solve the unbalanced problem. However, SLGS only considers the pixel information on the left and right sides of the target pixel without analyzing the information in other directions. Thus, the information in the extracted features is still insufficient to achieve a good recognition rate. For this issue, Dong et al. [10] proposed MOW-SLGS algorithm, which calculates the characteristic value of pixels around the target pixel in the 5 × 5 neighborhood in the direction of 0, 45, 90, and 135°, respectively, and gives the optimal weight. Finally, the maximum value of the four directions is

set as the eigenvalue. MOW-SLGS was shown to provide a reasonable recognition rate.

However, LGS and MOW-SLGS only choose several pixels in the neighborhood of 3 × 4 and 5 × 5. When computing the feature values, they do not consider all the pixels. This will lead to some information loss. To solve this problem, this chapter proposes a Local Cycle Graph Structure (LCGS) operator, which constructs the graph structure in the neighborhood of 3 × 3. The feature values of the target pixel are obtained by using all the pixels in its selected neighborhood. Due to the dimension of the matrix of the characteristic values is too large, the training for classification is not easy. Therefore, we employ the principal component analysis (PCA) [11, 12] method for dimensionality reduction through the experiments. We use the extreme learning machine (ELM) [13, 14] to classify and match the features after dimensionality reduction. Experimental results show that the LCGS algorithm performs better for face

The rest of this article is organized as follows. Section 2 introduces the technical details of LGS and MOW-SLGS; Section 3 gives the detailed algorithm of LCGS; Section 4 shows the experimental results on the ORL and AR database; Section 5 concludes this manuscript.

LGS algorithm [8] applied the graph structure in the calculation of the feature values, the main idea is as follows: take the center pixel as the target pixel, and take the two pixels of the left side and three pixels of the right side in the neighborhood of 3 × 4 to constitute the graph

issue for face recognition.

58 Machine Learning and Biometrics

occluded faces fairly well.

recognition with occlusion.

**2. Related theory**

**2.1. Local graph structure (LGS)**

**Figure 2.** The design of weights for MOW-SLGS.

**Figure 3.** Graph structure of MOW-SLGS in the direction of 45°.
