http://103.7.193.12:8080/xmlui/handle/123456789/133 2026-04-17T15:36:18Z http://103.7.193.12:8080/xmlui/handle/123456789/762 Kernel Choice for Unsupervised Kernel Methods Alam, Md. Ashad In kernel methods, choosing a suitable kernel is indispensable for favorable results. While cross-validation is a useful method of the kernel and parameter choice for supervised learning such as the support vector machines, there are no well-founded methods, have been established in general for unsupervised learning. We focus on kernel principal component analysis (kernel PCA) and kernel canonical correlation analysis (kernel CCA), which are the nonlinear extension of principal component analysis (PCA) and canonical correlation analysis (CCA), respectively. Both of these methods have been used effectively for extracting nonlinear features and reducing dimensionality. As a kernel method, kernel PCA and kernel CCA also suffer from the problem of kernel choice. Although cross-validation is a popular method of choosing hyperparameters, it is not applicable straightforwardly to choose a kernel and the number of components in kernel PCA and kernel CCA. It is important, thus, to develop a well-founded method for choosing hyperparameters of the unsupervised methods. In kernel PCA, it is not possible to use cross-validation for choosing hyperparameters because of the incomparable norms given by different kernels. The first goal of the dissertation is to propose a method for choosing hyperparameters in kernel PCA (the kernel and the number of components) based on cross-validation for the comparable reconstruction errors of pre-images in the original space. The experimental results of synthesized and real-world datasets demonstrate that the proposed method successfully selects an appropriate kernel and the number of components in kernel PCA in terms of visualization and classification errors on the principal components. The results imply that the proposed method enables the automatic design of hyperparameters in kernel PCA. XIV In recent years, the influence function of kernel PCA and a robust kernel PCA has been theoretically derived. One observation of their analysis is that kernel PCA with a bounded kernel such as Gaussian is robust in that sense the influence function does not diverged, while for kernel PCA with unbounded kernels for example polynomial the influence function goes to infinity. This can be understood by the boundedness of the transformed data onto the feature space by a bounded kernel. While this is not a result of kernel CCA but for kernel PCA, it is reasonable to expect that kernel CCA with a bounded kernel is also robust. This consideration motivates us to do some empirical studies on the robustness of kernel CCA. It is essential to know how kernel CCA is effected by outliers and to develop measures of accuracy. Therefore, we do intend to study a number of conventional robust estimates and kernel CCA with different functions but fixed parameter of kernel. The second goal of the dissertation is to discuss five canonical correlation coefficients and investigate their performances (robustness) by influence function, sensitivity curve, qualitative robustness index and breakdown point using different type of simulated datasets. The final goal of the dissertation is to extract the limitations of cross-validation for the kernel CCA, and to propose a new regularization approach to overcome the limitations of kernel CCA. As we demonstrate for Gaussian kernels, the cross-validation errors for kernel CCA tend to decrease as the bandwidth parameter of the kernel decreases, which provides inappropriate features with all the data concentrated in a few points. This is caused by the ill-posedness of the kernel CCA with the cross-validation. To solve this problem, we propose to use constraints on the 4th order moments of canonical variables in addition to the variances. Experiments on synthesized and real world datasets including human action recognition for a robot demonstrate that the proposed higher-order regularized kernel CCA can be applied effectively with the cross-validation to find appropriate kernel and regularization parameters. Methods using positive definite kernel (PDK), kernel methods play an increasingly prominent role to solve various problems in statistical machining learning such as, web design, pattern recognition, human action recognition for a robot, computational protein function perdition, remote sensing data analysis and in many other research fields. Due to the kernel trick and reproducing property, we can use linear techniques in feature spaces without knowing explicit forms of either the feature map or feature spaces. It offers versatile tools to process, analyze, and compare many types of data and offers state-of-the-art performance. Nowadays, PDK has become a popular tool for the most branches of statistical machine learning e.g., supervised learning, unsupervised learning, reinforcement learning, non-parametric inference and so on. Many methods have been proposed to kernel methods, which include support vector machine (SVM, Boser et al., 1992), kernel ridge regression (KRR, Saunders et al., 1998), kernel principal component analysis (kernel PCA, Schélkopf et al., 1998), kernel canonical correlation analysis (kernel CCA, Akaho, 2001, Bach and Jordan, 2002), Bayesian inference with positive definite kernels (kernel Bayes’ rule, Fukumizu et al., 2013), gradient-based kernel dimension reduction for regression (gKDR, Fukumizu and Leng, 2014), kernel two-sample test (Gretton, 2012) and so on. 2014-09-01T00:00:00Z http://103.7.193.12:8080/xmlui/handle/123456789/352 Kernel Choice for Unsupervised Kernel Methods Alam, Md. Ashad In kernel methods, choosing a suitable kernel is indispensable for favorable results. While cross-validation is a useful method of the kernel and parameter choice for supervised learning such as the support vector machines, there are no well-founded methods, have been established in general for unsupervised learning. We focus on kernel principal component analysis (kernel PCA) and kernel canonical correlation analysis (kernel CCA), which are the nonlinear extension of principal component analysis (PCA) and canonical correlation analysis (CCA), respectively. Both of these methods have been used effectively for extracting nonlinear features and reducing dimensionality. Methods using positive definite kernel (PDK), kernel methods play an increasingly prominent role to solve various problems in statistical machining learning such as, web design, pattern recognition, human action recognition for a robot, computational protein function perdition, remote sensing data analysis and in many other research fields. Due to the kernel trick and reproducing property, we can use linear techniques in feature spaces without knowing explicit forms of either the feature map or feature spaces. It offers versatile tools to process, analyze, and compare many types of data and offers state-of-the-art performance. Nowadays, PDK has become a popular tool for the most branches of statistical machine learning e.g., supervised learning, unsupervised learning, reinforcement learning, non-parametric inference and so on. Many methods have been proposed to kernel methods, which include support vector machine (SVM, Boser et al., 1992), kernel ridge regression (KRR, Saunders et al., 1998), kernel principal component analysis (kernel PCA, Schélkopf et al., 1998), kernel canonical correlation analysis (kernel CCA, Akaho, 2001, Bach and Jordan, 2002), Bayesian inference with positive definite kernels (kernel Bayes’ rule, Fukumizu et al., 2013), gradient-based kernel dimension reduction for regression (gKDR, Fukumizu and Leng, 2014), kernel two-sample test (Gretton, 2012) and so on. During the last decade, unsupervised learning has become an important application area of the kernel methods. There are two most powerful tools of unsupervised kernel methods, namely kernel principal component analysis (kernel PCA) and kernel canonical correlation analysis (kernel CCA) (Schélkopf et al., 1998, Akaho, 2001). 2014-09-01T00:00:00Z http://103.7.193.12:8080/xmlui/handle/123456789/152 STATISTICAL ANALYSIS OF FOOD CONSUMPTION BEHAVIOUR IN SELECTED AREAS OF BANGLADESH: AN EMPIRICAL STUDY MAJUMDER , UTTAM KUMAR The present study applied different statistical tools to identify the socio-economic and demographic factors affecting child malnutrition, food consumption and nutrients intake pattern of the households and to suggest measures to improve the present dietary intake pattern towards food security of the rural households in Bangladesh. The study was carried out on all households randomly selected from two villages from Dinajpur as a rice surplus district and all the households of two villages from Bagerhat as a rice deficit district using a three-stage random sampling scheme. Information about socio-demographic and economic characteristics of the households was collected by using a structured questionnaire. Food consumption data were collected through 24 hours recall and partly by weighing method. Height, weight and mid arm circumference of all the children under 6 years of age from the study population were measured using standardized instruments. Bangladesh has been facing the chronic food deficit for many years. In the past, Bangladesh has suffered poverty, frequent natural disasters, and rapid population growth and there has been a gradual decline in per capita nutrient intake. Traditional dietary practices have undergone significant changes since 1937, which has contributed to the decline of nutrient uptake. In 1937, rice was the chief component of the diet at the village level, with protein supplied by lentils, peas, Bengal gram, green gram, black gram, cowpea and kheshari etc. But the daily nutrient intake of poor people was better than that of today. Massive starvation during the famine in 1943 caused a change in dietary practices. People began to eat green leaves, roots, tubers, and many unfamiliar foods because of the scarcity of cereals and the sharp increase in the price of rice. In 1971, in the refugee camp in India, both adults and children ate unfamiliar foods and gradually accustomed themselves to using wheat as their staple diet. In 1974 and 1977, crop failure and flood in Bangladesh caused more changes in food habits and dietary food consumption pattern (Roy and Haider, 1988). This was associated with natural calamities that adversely affected the production of rice and other crops in the country almost every year and the newly born country experienced an acute food shortage. 2009-12-01T00:00:00Z http://103.7.193.12:8080/xmlui/handle/123456789/136 MEASURING EFFICIENCY OF WHEAT PRODUCTION IN NORTHERN REGION OF BANGLADESH: A STOCHASTIC FRONTIER FUNCTION ANALYSIS Khondaker, Md. Earfan Ali The main objective of the present study was to identify and analyze the possibilities for improving productivity of wheat by increasing the farmers’ productive efficiency. The efficiency of wheat farmers in the northern region of Bangladesh was measured through the estimation of stochastic frontier production function used by cross-sectional data for the 2007-2008 crop year. The attempt of the study was also to determine some socio-economic characteristics and management practices which influence technical efficiency of wheat production. Technical efficiency was defined as the ratio of the observed output to the corresponding frontier and was estimated from the composed error term. Variations in the technical efficiency index across the production units were explained through a number of farmers and farm characteristics’ variables following Battese and Coelli (1995) and incorporating the sprit of Rougoor et al. (1998). The yield of wheat varied across location, farmer and farm categories. The average yield was 3503 kg/ha with the highest average by trained farmers. It was actually for the adoption of new technologies, new varieties (HYV) and favorable climate. Fields recording higher yields were sown timely and received more fertilizers, manure and irrigation. Other socio-agro-economic factors also played roles in the variation in yields. The biophysical constraints limiting wheat production were lack of quality seed, excessive weed, poor utilisation of irrigation facilities, etc. The estimates of a generalised stochastic frontier production function models showed that fertiliser, FYM and irrigation had significant positive impacts on wheat production. The maximum likelihood method is applied for the estimation of the parameters of the model and the prediction of the technical efficiencies of the farms and farm-specific Cobb-Douglas stochastic normalized cost frontier and economic inefficiency effects over time. The mean farm-specific technical allocative and economic efficiency of wheat growers were unit’s ranging from 44 to 97%. The coefficient of farmers’ education, wheat farming experience and training on wheat cultivation were negatively associated in the inefficiency effect models implying that efficiency increases with the increase of farmers’ education, wheat farming experience and training on wheat production. Trained farmers adopted more recommended wheat technologies and achieved higher yield. The results indicated that the majority of wheat farmers in northern region of Bangladesh operated close to the maximum technically feasible yield levels and that there was limited potential to improve technical efficiency. Perhaps the most contemporary interest was that farmers considered maintaining the environment as an important objective achieved higher level of technical efficiency. The study suggests that the frontier farmers received higher yields following optimum seeding time, using more fertiliser, manure and applying timely irrigation with modest use of seed rate, and human labour. However, for sustainable wheat yield and production more emphasis should be given on updating farmers’ knowledge through proper training/orientations. he agriculture sector plays a crucial role in the development of Bangladesh. It shares 15.6% of the GDP and employs about 43.6% of the workforce in the country. Wheat is one of the main cereal crops in the world as well as in Bangladesh. The average daily per capita calorie intake is 2240 kilocalories (estimated) per individual. Thus the people of the region get a significant calorie from wheat. About 4.5% of the total cultivable land is utilized here for wheat production. Wheat production in the country in year 2009-2010 was around 1.07 million tons from 0.37 million hectares but the total demand was 3.0-3.5 million tons. Bangladesh needs to import about 2.0-2.5 million tons wheat every year. Moreover, wheat consumption growth rate is 4.3% per year (BBS 2010). It is grown in more than 240 million hectares in the world, an area larger than that of any other crop (Hanson et al.1982). It contributes more calories and protein than any other food crop. World trade in wheat exceeds all other grains produced. Sharp raised wheat area in many developing countries as well as in Bangladesh also indicates its importance. Form 1963 to 1980 wheat area and production increased by 9.3 and 15.5 percent per year, respectively (Hanson et al. 1982). Wheat area and production also continued to increase until 1999. For the last thirty-four years of post independence period of Bangladesh, annual growth rate of area, production and yields were 12.70, 8.82 and 24.93 percent, respectively (Table 1.1). Starting with an area 0.126 million hectares and production of 0.11 million tons in 1971, the area and production increased to 0.84 million hectares 1.84 million tons, respectively, in 2000. The yields also increased from 860 kg/ha to 2210 kg/ha during the period. This increased area, production and yield of wheat spurred mainly because of the introduction of modern seed-water-fertiliser technologies. After reaching its highest area (0.87 million hectare) and production (1.9 million tons) in 1999, the area and production was found to be decreasing during next five years. In 2004, the area decreased to 0.64 million hectares and production to 1.2 million tons. The yields also reduced to 1952 kg/ha (BBS 2005). In 2010, the area decreased to 0.37 million hectares and production to 1.07 million tons. The yields also increased from 1952 kg/ha to 3500 kg/ha from new varieties and production technology during the period (BBS 2010). 2006-01-01T00:00:00Z