مولوی نورالہدیٰ ندوی بہاریؔ
مولانا عبدالرحمان مرحوم کے ماتم سے ابھی آنکھیں خشک نہیں ہوئی تھیں کہ ہم کو ندوہ کے ایک دوسرے قابل فرزند مولوی نورالہدیٰ ندوی کے ماتم میں اشک بار ہونا پڑا، جو مقاصد ندوہ کی تکمیل میں ابھی تگ ودو کررہا تھا، مرحوم نے تقریباً سات سال تک ندوہ میں عربی کی تعلیم حاصل کی، پھر تین سال مدرسۂ الٰہیات کانپور میں بسر کرکے انگریزی شروع کی اور اس سال بی اے آنر کا امتحان دیا تھا اور اس کے بعد ہم ان سے مقاصد ندوہ کے مطابق ہر قسم کی علمی توقعات قائم کرسکتے تھے، جن کے آثار ان کی زندگی کے نہایت ابتدائی دور سے نمایاں تھے اور تعلیمی ترقی کے ساتھ ساتھ ان میں بھی تدریجی ترقی ہوتی جاتی تھی، چنانچہ وہ پہلے ندوہ میں طلبہ کے قلمی رسالہ الاصلاح کے اڈیٹر رہے، پھر کلکتہ میں ایک روزنامہ کو اڈٹ کیا، رسالہ حور جو کلکتہ سے نکل کر چند ماہ کے بعد بند ہوگیا، انہیں کے دست و بازو کے بل پر نکلتا رہا۔ معارف میں بھی انہوں نے بعض مضامین لکھے تھے، لیکن اب تکمیل کے بعد جب کہ یہ توقعات باضابطہ اور مستقل صورت اختیارکرتیں:
این ماتم سخت است کہ گویند جوان مرد
(سید سليمان ندوی،جون ۱۹۲۶ء)
يقوم الخطاب الأدبي على عنصرين أساسيين، وهما: (الصوت والمعنى)، إذ أنّ أحدهمالا ينفكّ عن الآخر، وبلحاظ الترابط ما بين هذين العنصرين نتلمّس أنّ الخطابة: هي ذلك الفن الّذي يتوقّف تحققه على المواجهة والمشافهة، حيث أنّ الإلقاء يؤثر بشكل ملحوظ على المتلقّي، موازنة بالكيفيّة الّتي يكون بها المتلقّي مع الكتابة، بالتالي فإنّ حجم التأثير النّفسي والعاطفي والتركيز والشّد الذهني حين الاستماع إلى خطبة معيّنة أكبر عند المتلقّي ممّا هوَ عليه حين القراءة لسطور معيّنة. لذا فإن إبداع المتكلّم يتحقّق في التكلّم بخطبة ما، وهذا بحد ذاته إنما هوَ استظهار للعمق الدلالي والفكري، والاستعمال الفنّي للأدوات الصّوتية، وأصدق تمثيل لما تقدّم هو الاستماع إلى الشعر والنثر. وموضوع بحثنا هوَ الأسلوب الخطابي لفارس الخطابة ومنشأها، الّذياجتمع فيه ما لم يجتمع في غيره، حتى بلغ أسلوبه من الصدق مستوىً ترفّع به عن السّجع المتكلّف، فبأسلوبه إنّما هوَ أبعد متكلّم عن التصنّع، وأقرب ما يكون من الصراحة والصدق في القول والفعل.
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.