تحقیقات حدیث میں پروفیسر جوزف شاخت کی طرز تحقیق کا تنقیدی جائزہ

In general, the results of research studies conducted by Professor Joseph Schacht and his fellows on criticism of Ahadith are contradictory with the results of Muslim Scholars. Muslim Scholars, point of view is that Muhaddithin have opposed, with full power, the condemnable tries for fabrication of Ahadith. Valuable principles for the identification of authentic and unauthentic traditions were the result of the struggles done by Muhaddithin. With the help of these principles the categorization of Ahadith came in to practical. Professor Joseph Schacht argues that the material presented as Ahadith and Sunna of Prophet by Muslim scholars is the production of later times. According to his point of view, there is no authentic hadith in the bulk of traditions and if assumed that there are few authentic, they are also mixed up with unauthentic and there is no possibility of identification of authentic one. This study is a try to identify the mistakes of his research approach.

Image Clustering Using Novel Local and Global Exponential Discriminant Models

Image clustering deals with the optimal partitioning of images into different groups. Using linear discriminant analysis (LDA) criterion, optimal partitioning of images is obtained by maximizing the ratio of between-class scatter matrix (Sb) to within-class scatter matrix (Sw). In global learning based clustering models, scatter matrices (Sb and Sw) were evaluated on whole image datasets. Owing to which, nonlinear manifold in image datasets may not be effectively handled. For manifold learning, local neighborhood information in data objects were utilized in local learning based clustering models. Further, for high-dimensional data, Sw is singular which corresponds to under-sampled or small-sample-size (SSS) problem of LDA. Owing to which, almost all global learning and local learning based clustering models are based on regularized discriminant analysis (RDA), a variant of LDA. In RDA, the singularity problem of Sw was solved by perturbing it with regularization parameter λ > 0. However, tuning for optimal value of parameter λ is required. Further, for optimal clustering performance in existing state-of-the-art local learning based clustering models, one has to tune a number of clustering parameters from a large candidate set. In this thesis, we propose a novel local learning based image clustering model. Our proposed clustering model is inspired from exponential discriminant analysis (EDA). EDA is another variant of LDA in which SSS problem of LDA was handled using matrix exponential properties. Owing to which, EDA is less parameterized as compared with RDA. Number of nearest neighbor images k is the only clustering parameter in our proposed clustering model as compared with existing state-of-the-art local learning based clustering models. Image clustering performances on 12 benchmark image datasets are comparable over near competitor RDA based image clustering model. Performances are comparable because no discriminant information of LDA is lost in EDA. However, well separated images may not be achieved at local level for image datasets that contain images with pose, illumination, or xiv occlusion variations. Owing to which, local learning based image clustering models may face limitations in such variations. For this problem, various clustering models were proposed in which both global learning and local learning approaches were utilized. However, almost all existing local and global learning based clustering models are based on RDA. Owing to which, tuning of clustering parameters is extensive in almost all state-of-the-art local and global learning based image clustering models. We propose novel local and global learning based image clustering models that are inspired from EDA. Our proposed image clustering models are less-parameterized and computationally efficient where image clustering performances are comparable with existing local and global learning based clustering models. However, performances of all state-of-the-art clustering models are not optimal for challenging image datasets that contain images with illumination and occlusion changes. We explore the challenges in image clustering problem. We show that variation from one image to another image in a class (within-class variation) of an image dataset may vary from nominal to significant due to images with different facial expressions, pose, illumination, or occlusion changes. Using pixel intensity values as image features, we obtain histogram of within-class variation for each image datasets. On the basis of histogram, we categorize image datasets as Gaussian-like or multimodal. We show that image clustering performances of state-of-the-art clustering models are optimal for Gaussian-like image datasets and it degrade significantly for multimodal image datasets. We achieved significant overall performance improvement on 13 benchmark image datasets by employing optimal image descriptors with our proposed clustering model. Our study shows that there is no direct correlation between image clustering performance and local neighborhood structure. However, image clustering performance has correlation with the distribution of within-class variation in image datasets.