Abstract: A method and a system for recognizing faces have been disclosed. The method may comprise: retrieving a pair of face images; segmenting each of the retrieved face images into a plurality of image patches, wherein each patch in one image and a corresponding one in the other image form a pair of patches; determining a first similarity of each pair of patches; determining, from all pair of patches, a second similarity of the pair of face images; and fusing the first similarity determined for the each pair of patches and the second similarity determined for the pair of face images.

Abstract: A method and a system for recognizing faces have been disclosed. The method may comprise: retrieving a pair of face images; segmenting each of the retrieved face images into a plurality of image patches, wherein each patch in one image and a corresponding one in the other image form a pair of patches; determining a first similarity of each pair of patches; determining, from all pair of patches, a second similarity of the pair of face images; and fusing the first similarity determined for the each pair of patches and the second similarity determined for the pair of face images.

Abstract: An exemplary method for extracting discriminant feature of samples includes providing data for samples in a multidimensional space; based on the data, computing local similarities for the samples; mapping the local similarities to weights; based on the mapping, formulating an inter-class scatter matrix and an intra-class scatter matrix; and based on the matrices, maximizing the ratio of inter-class scatter to intra-class scatter for the samples to provide discriminate features of the samples. Such a method may be used for classifying samples, recognizing patterns, or other tasks. Various other methods, devices, system, etc., are also disclosed.

Abstract: Systems and methods perform Laplacian Principal Components Analysis (LPCA). In one implementation, an exemplary system receives multidimensional data and reduces dimensionality of the data by locally optimizing a scatter of each local sample of the data. The optimization includes summing weighted distances between low dimensional representations of the data and a mean. The weights of the distances can be determined by a coding length of each local data sample. The system can globally align the locally optimized weighted scatters of the local samples and provide a global projection matrix. The LPCA improves performance of such applications as face recognition and manifold learning.

Abstract: Described is using semi-Riemannian geometry in supervised learning to learn a discriminant subspace for classification, e.g., labeled samples are used to learn the geometry of a semi-Riemannian submanifold. For a given sample, the K nearest classes of that sample are determined, along with the nearest samples that are in other classes, and the nearest samples in that sample's same class. The distances between these samples are computed, and used in computing a metric matrix. The metric matrix is used to compute a projection matrix that corresponds to the discriminant subspace. In online classification, as a new sample is received, it is projected into a feature space by use of the projection matrix and classified accordingly.

Abstract: A method for modeling data affinities and data structures. In one implementation, a contextual distance may be calculated between a selected data point in a data sample and a data point in a contextual set of the selected data point. The contextual set may include the selected data point and one or more data points in the neighborhood of the selected data point. The contextual distance may be the difference between the selected data point's contribution to the integrity of the geometric structure of the contextual set and the data point's contribution to the integrity of the geometric structure of the contextual set. The process may be repeated for each data point in the contextual set of the selected data point. The process may be repeated for each selected data point in the data sample. A digraph may be created using a plurality of contextual distances generated by the process.

Abstract: Described is using semi-Riemannian geometry in supervised learning to learn a discriminant subspace for classification, e.g., labeled samples are used to learn the geometry of a semi-Riemannian submanifold. For a given sample, the K nearest classes of that sample are determined, along with the nearest samples that are in other classes, and the nearest samples in that sample's same class. The distances between these samples are computed, and used in computing a metric matrix. The metric matrix is used to compute a projection matrix that corresponds to the discriminant subspace. In online classification, as a new sample is received, it is projected into a feature space by use of the projection matrix and classified accordingly.

Abstract: An exemplary method for extracting discriminant feature of samples includes providing data for samples in a multidimensional space; based on the data, computing local similarities for the samples; mapping the local similarities to weights; based on the mapping, formulating an inter-class scatter matrix and an intra-class scatter matrix; and based on the matrices, maximizing the ratio of inter-class scatter to intra-class scatter for the samples to provide discriminate features of the samples. Such a method may be used for classifying samples, recognizing patterns, or other tasks. Various other methods, devices, system, etc., are also disclosed.

Abstract: A method for modeling data affinities and data structures. In one implementation, a contextual distance may be calculated between a selected data point in a data sample and a data point in a contextual set of the selected data point. The contextual set may include the selected data point and one or more data points in the neighborhood of the selected data point. The contextual distance may be the difference between the selected data point's contribution to the integrity of the geometric structure of the contextual set and the data point's contribution to the integrity of the geometric structure of the contextual set. The process may be repeated for each data point in the contextual set of the selected data point. The process may be repeated for each selected data point in the data sample. A digraph may be created using a plurality of contextual distances generated by the process.

Abstract: Systems and methods perform Laplacian Principal Components Analysis (LPCA). In one implementation, an exemplary system receives multidimensional data and reduces dimensionality of the data by locally optimizing a scatter of each local sample of the data. The optimization includes summing weighted distances between low dimensional representations of the data and a mean. The weights of the distances can be determined by a coding length of each local data sample. The system can globally align the locally optimized weighted scatters of the local samples and provide a global projection matrix. The LPCA improves performance of such applications as face recognition and manifold learning.