Gaussian distribution

Tsallis statistics (or q-statistics) in nonextensive statistical mechanics is a one-parameter description of correlated states. In this paper we use a translated entropic index: $1 - q \to q$ . The essence of this translation is to improve the mathematical symmetry of the q-algebra and make q directly proportional to the nonlinear coupling. A conjugate transformation is defined $\hat q

Powders and granulated solids are widely used in industrial bulk solids storage, handling, and transportation systems. Such bulk materials handling operations frequently involve a falling stream of material. During such a process, the surrounding air is induced to flow with the falling particle stream, forming a particle-driven plume. Herein, experimental research results are reported on this fundamental problem, focusing in

We discuss types of clustering problems where error information associated with the data to be clustered is readily available and where error-based clustering is likely to be superior to clustering methods that ignore error. We focus on clustering derived data (typically parameter ...

Distribusi Multivariate Normal (Gaussian) adalah salah satu distribusi yang sering
digunakan, mengingat hampir semua kejadian bisa didekati dengan distribusi tersebut. Dalam
mengenali suatu objek dalam bentuk image, fitur objek tersebut kerapkali mengikuti distribusi
  Multivariate Gaussian dengan parameter mean dan covariance yang berbebeda-beda.
  Parameter dan yang berbeda-beda tersebut akan menghasilkan nilai probability density
function (pdf) yang berbeda pula. Berdasarakan nilai probability density function ini
selanjutnya dapat dibentuk fungsi diskriminan untuk mengenali objek (Gaussian Classifier).
Kehandalan Gaussian Classifer dalam mengenali objek dalam bentuk image dipengaruhi oleh
2 faktor utama yaitu ketepatan dan keakuratan dalam pengambilan data objek training yang
akan berpengaruh terhadap ketepatan dan keakuratan fitur yang diambil dan asumsi distribusi
Multivariate Normal dari fitur objek yang diambil harus terpenuhi. Untuk memenuhi asumsi
multivariate distribusi Multivariate Normal maka harus dilakukan pengujian terhadap
normalitas distribusi fitur setiap kelas objek.

Content-Based Image Retrieval (CBIR) systems are required to effectively harness infor- mation from ubiquitous image collections. Despite intense research efforts by the multidis- ciplinary CBIR community since early 1990s, apparently there is a mismatch between these advances and the one that is truly required to bring success to CBIR in the commercial mar- ket place. In this paper we provide

Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.