# Robust Face Recognition Based on a New Supervised Kernel Subspace Learning Method
## 1 Introduction
However, these kernel-based methods cannot directly consider the local data structure, which results in classification performance degradation. Recently, the locality preserving projections (LPP) method has been proposed as a linear subspace learning method to address the out-of-sample problem [37]. LPP is an unsupervised linear subspace technique that has the remarkable advantage of being able to generate an explicit map. Similar to the one belonging to PCA and LDA, this map is linear and easy to compute, and is also effective for many face recognition tasks. Although LPP is designed based on \"locality,\" like most manifold learning methods, it still suffers from the \"over learning of locality\" problem, because there is no direct connection with classification in its algorithm. Therefore, on some occasions, it cannot be guaranteed to map an appropriate projection for classification purposes [37]. Subsequently, in order to address this issue and delve into more influential projections for classification tasks, the unsupervised discriminant projection (UDP) method was developed as a simple version of LPP [38]. UDP is considered a linear estimation of multi-manifold-based learning because it considers both the local and nonlocal scatters of data. In both LPP and UDP, the data class label information is not considered, which may degrade their pattern classification performance. Furthermore, the discriminant neighborhood embedding (DNE) method has been presented with the idea of using data class label information [39]. DNE can find a good embedding for classification, considering intra-class absorption and inter-class class expulsion. The main characteristic of DNE is called \"discrimination,\" meaning the ability to distinguish the same class from distinct classes. This specification of DNE can deal well with \"out-of-sample\" and \"small training sample size\" problems. Nevertheless, DNE cannot correctly preserve local information of data because it only concedes \(+1\) and \(-1\) to intra-class and inter-class neighbors [15]. Thus, much of the important geometrical structure information of data may be lost, and it might fail to find out the most significant sub-manifolds for pattern recognition. The locality-based discriminant neighborhood embedding method (LDNE) has recently been proposed to tackle the problems existing in LPP and DNE [15]. This method takes into account both the \"locality\" and the \"discrimination\" in a united modelling environment. However, many important non-linear data might be lost during the dimensionality reduction process, which dramatically influences classification accuracy. According to the way dimensionality reduction algorithms \"learn\" from data to create predictions, they can be categorized into two different classes: supervised and unsupervised learning methods. Among these two, supervised machine learning is used more prevalently. In this case, the data scholar acts as a guide to instruct the algorithm regarding which results should be found by it [40]. The most well-known supervised algorithms include supervised LPP [39], local discriminant embedding (LDE) [41], neighborhood discriminant projection (NDP) [42], discriminant locality preserving projections (DLPP) [43], locally discriminating projection (LDP) [44], and geometry preserving projections (GPP) [45] It is clear that the aforementioned supervised techniques generally apply class label information in order to amend the dimensionality reduction. On the other hand, the unsupervised LPP-based algorithms generally aim to improve the locality preserving and discriminating capabilities to further enhance the final performance of the classification process. Graph-optimized locality preserving projections (GOLPP) [15; 46], orthogonal locality preserving projection (OLPP) [47], and UDP [38] are some examples of the unsupervised LPP-based methods. In this project, a new supervised subspace learning algorithm named \"supervised kernel locality-based discriminant neighborhood embedding\" (SKLDNE) is proposed.