| Measurement is one of the hot issues in the field of machine learning. The performance of many machine learning algorithms is heavily dependent on the measurement data, such as KNN algorithm. Measure learning which can learn specific tasks and as a kind of data measurement method has been widely used for classification, clustering and information retrieval, and other fields. With the development of machine learning theory and the complication and diversification of study tasks, metric learning have also made many achievements and formed a huge framework. But most of these algorithms are ID algorithm that based on vector data. When processing structured matrix data that also will be processed after vectorization which ignoring the inner space structure information of matrix-form data. To make full use of the spatial information of matrix-form data, the most direct method is calculated using the matrix data directly, namely 2D algorithm based on matrix data. Since the Principal Component Analysis (1D-PCA) extended to the image oriented 2D-PCAby Yang et al, a number of 1D methods have been extended to their corresponding 2D variants. From the broad perspective there are already some 2D measuring learning algorithm, but the existing 2D algorithm does not have generality, and there is still no corresponding 2D form of the global measure learning algorithm based on constraint in pairs.Based on the basis of the global measure learning algorithm basing on constraints in pairs, this paper put forward the 2D measuring learning algorithm. Its main characteristic is calculated using the matrix data, and through a structured metric matrix reflects the spatial structure information of matrix-form data. The experiment result show that when the processing image data, the 2D algorithm obtained better performance than the original method of 1D.Even though the 2D algorithm's performance is much better than the 1D algorithm's in many filed, However, the 2D methods still suffer from two main drawbacks:(1) they are almost all linear, which might not match the nonlinear structure of actual data; and (2) the spatial information of data is not fully used in existing 2D methods.To address the first drawback, although the kernel trick is theoretically feasible, it is practically difficult since the representation theorem cannot be straightforwardly extended for 2D-form data. To this end, we in this work propose to obtain a simple kemelizing method by changing the measurement without the representation theorem. In view of the second shortcoming, this paper aim to use the spatial information of data in the nonlinear mapping feature space (or say kernel space). Unfortunately, it usually requires to describe the data in the nonlinear feature space (i.e., kernel space), which is generally implemented through data dimension-increasing as well as implicit kernel mapping. To fulfill this goal, it usually refers to the implicit or explicit kernel mapping, the former, however, might distort the spatial structure of data while the latter leads to dimension risk. As a result, we can preferably preserve the spatial structure of data naturally if we employ the form of explicit kernels in which the dimension is identical and each component is uncoupled. Fortunately, many explicit kernel (e.g., Hellinger and Euler kernels) and approximate explicit mathematical formulations of some implicit additive kernels (e.g., Intersection, JS and ?2 kernels) meet the requirements. This paper attempt to kernelizing matrix-form data by Euler kernel and compensate the spatial information in the mapped kernel space. Although there exist various ways to compensating the spatial information, e.g., spatial structure information constraints and image distance metric, we in this work take the Image Euclidean Distance as an example to carry out the study and then develop matrix/image-oriented Spatial Euler Kernel. |
PDF Full Text Request