Classification via semi-Riemannian spaces

In this paper, we develop a geometric framework for linear or nonlinear discriminant subspace learning and classification. In our framework, the structures of classes are conceptualized as a semi-Riemannian manifold which is considered as a submanifold embedded in an ambient semi-Riemannian space. The class structures of original samples can be characterized and deformed by local metrics of the semi-Riemannian space. Semi-Riemannian metrics are uniquely determined by the smoothing of discrete functions and the nullity of the semi-Riemannian space. Based on the geometrization of class structures, optimizing class structures in the feature space is equivalent to maximizing the quadratic quantities of metric tensors in the semi-Riemannian space. Thus supervised discriminant subspace learning reduces to unsupervised semi-Riemannian manifold learning. Based on the proposed framework, a novel algorithm, dubbed as Semi-Riemannian Discriminant Analysis (SRDA), is presented for subspace-based classification. The performance of SRDA is tested on face recognition (singular case) and handwritten capital letter classification (nonsingular case) against existing algorithms. The experimental results show that SRDA works well on recognition and classification, implying that semi-Riemannian geometry is a promising new tool for pattern recognition and machine learning. 1

Penerapan Pendekatan Pengajaran Terbalik (Reciprocal Teaching) Untuk Meningkatkan Kemandirian Belajar Biologi Siswa Kelas Vii-g SMP N 5 Karanganyar Tahun Pelajaran 2010/ 2011

– The objective of this study is to improve student independence in learning biology by implementing Inverted Teaching Approach (Reciprocal Teaching) on Environmental Management material. This research is a classroom action research. This research was conducted in two cycles. Each cycle consisted of planning, implementation of the action,observation, and reflection. The subjects of the study were VII-G class students of SMP Negeri 5 Karanganyar in the academic year of 2010/2011. The number of the students was 32. The technique and instrumen of collectiing data were questionnaire, observation, and interviews. The technique of analyzing data was descriptive analysis techniques. Triangulation technique was used in data validation. The results proved that by implementing Inverted Teaching Approach (Reciprocal Teaching) students\u27 independence in learning biology enhanced. It is based on the results of questionnaires, observations and interviews. The questionnaire of students\u27 learning independence showed that the mean percentage of students\u27 achievement in each indicator in pre-cycle, cycle I, and cycle II was 67.97%, 72.55%, and 77.58% respectively. The observation of students\u27 learning independence showed that the mean percentage of students\u27 achievement in each indicator in pre-cycle, cycle I, and cycle II was 39.68%, 67.5%, and 80.62% respectively. It can be concluded that the implementation of Inverted Teaching Approach (Reciprocal Teaching) can enhance students learning independence

Laplacian PCA and its applications

Dimensionality reduction plays a fundamental role in data processing, for which principal component analysis (PCA) is widely used. In this paper, we develop the Laplacian PCA (LPCA) algorithm which is the extension of PCA to a more general form by locally optimizing the weighted scatter. In addition to the simplicity of PCA, the benefits brought by LPCA are twofold: the strong robustness against noise and the weak metric-dependence on sample spaces. The LPCA algorithm is based on the global alignment of locally Gaussian or linear subspaces via an alignment technique borrowed from manifold learning. Based on the coding length of local samples, the weights can be determined to capture the local principal structure of data. We also give the exemplary application of LPCA to manifold learning. Manifold unfolding (non-linear dimensionality reduction) can be performed by the alignment of tangential maps which are linear transformations of tangent coordinates approximated by LPCA. The superiority of LPCA to PCA and kernel PCA is verified by the experiments on face recognition (FRGC version 2 face database) and manifold (Scherk surface) unfolding. 1

Linear Laplacian Discrimination for Feature Extraction

Discriminant feature extraction plays a fundamental role in pattern recognition. In this paper, we propose the Lin-ear Laplacian Discrimination (LLD) algorithm for discrim-inant feature extraction. LLD is an extension of Linear Discriminant Analysis (LDA). Our motivation is to address the issue that LDA cannot work well in cases where sam-ple spaces are non-Euclidean. Specifically, we define the within-class scatter and the between-class scatter using similarities which are based on pairwise distances in sam-ple spaces. Thus the structural information of classes is contained in the within-class and the between-class Lapla-cian matrices which are free from metrics of sample spaces. The optimal discriminant subspace can be derived by con-trolling the structural evolution of Laplacian matrices. Ex-periments are performed on the facial database for FRGC version 2. Experimental results show that LLD is effective in extracting discriminant features. 1

2013 IEEE International Conference on Computer Vision Face Recognition via Archetype Hull Ranking

The archetype hull model is playing an important role in large-scale data analytics and mining, but rarely applied to vision problems. In this paper, we migrate such a geometric model to address face recognition and verification together through proposing a unified archetype hull ranking framework. Upon a scalable graph characterized by a compact set of archetype exemplars whose convex hull encompasses most of the training images, the proposed framework explicitly captures the relevance between any query and the stored archetypes, yielding a rank vector over the archetype hull. The archetype hull ranking is then executed on every block of face images to generate a blockwise similarity measure that is achieved by comparing two different rank vectors with respect to the same archetype hull. After integrating blockwise similarity measurements with learned importance weights, we accomplish a sensible face similarity measure which can support robust and effective face recognition and verification. We evaluate the face similarity measure in terms of experiments performed on three benchmark face databases Multi-PIE, Pubfig83, and LFW, demonstrating its performance superior to the state-of-the-arts. 1