A CHARACTERIZATION OF CONVEX FUNCTIONS AND ITS APPLICATION TO OPERATOR MONOTONE FUNCTIONS
We give a characterization of convex functions in terms of dier- ence among values of a function. As an application, we propose an estimation of operator monotone functions: If A > B 0 and f is operator monotone on (0,1), then f(A) f(B) f(kBk+ ) f(kBk) > 0, where = k(A B) 1 k 1 .
The Riemannian mean and matrix inequalities related to the Ando-Hiai inequality and chaotic order
The Riemannian mean on the convex cone of positive definite matrices is a kind of geometric mean of n -matrices which is an extension of the geometric mean of two-matrices. In this paper, we derive the Ando-Hiai inequality for the Riemannian mean which is an extension of the well-known Ando-Hiai inequality of two-matrices. Moreover, we shall show an extension of a characterization of chaotic order. Lastly, we will give a negative answer for the problem whether the same results are satisfied or not for other geometric means of n -matrices. Mathematics subject classification (2010): Primary 47A64; Secondary 47A63, 47L25.
Application of SVM on satellite images to detect hotspots in Jharia coal field region of India
The present paper deals with the application of Support Vector Machine (SVM) and image analysis techniques on NOAA/AVHRR satellite image to detect hotspots on the Jharia coal field region of India. One of the major advantages of using these satellite data is that the data are free with very good temporal resolution; while, one drawback is that these have low spatial resolution (i.e., approximately 1.1 km at nadir). Therefore, it is important to do research by applying some efficient optimization techniques along with the image analysis techniques to rectify these drawbacks and use satellite images for efficient hotspot detection and monitoring. For this purpose, SVM and multi-threshold techniques are explored for hotspot detection. The multi-threshold algorithm is developed to remove the cloud coverage from the land coverage. This algorithm also highlights the hotspots or fire spots in the suspected regions. SVM has the advantage over multi-thresholding technique that it can learn patterns from the examples and therefore is used to optimize the performance by removing the false points which are highlighted in the threshold technique. Both approaches can be used separately or in combination depending on the size of the image. The RBF (Radial Basis Function) kernel is used in training of three sets of inputs: brightness temperature of channel 3, Normalized Difference Vegetation Index (NDVI) and Global Environment Monitoring Index (GEMI), respectively. This makes a classified image in the output that highlights the hotspot and non-hotspot pixels. The performance of the SVM is also compared with the performance obtained from the neural networks and SVM appears to detect hotspots more accurately (greater than 91% classification accuracy) with lesser false alarm rate. The results obtained are found to be in good agreement with the ground based observations of the hotspots. This type of work will be quite helpful in the near future to develop a hotspots monitoring system using these operational satellites data.