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Low-rank matrix approximation is an effective tool in alleviating the memory and computational burdens of kernel methods and sampling, as the mainstream of such algorithms, has drawn considerable attention in both theory and practice. This paper presents detailed studies on the Nyström sampling scheme and in particular, an error analysis that directly(More)
Maximum margin clustering (MMC) is a recent large margin unsupervised learning approach that has often outperformed conventional clustering methods. Computationally, it involves non-convex optimization and has to be relaxed to different semidefinite programs (SDP). However, SDP solvers are computationally very expensive and only small data sets can be(More)
Kernel (or similarity) matrix plays a key role in many machine learning algorithms such as kernel methods, manifold learning, and dimension reduction. However, the cost of storing and manipulating the complete kernel matrix makes it infeasible for large problems. The Nyström method is a popular sampling-based low-rank approximation scheme for reducing the(More)
The Nyström method is a well-known sampling-based technique for approximating the eigensystem of large kernel matrices. However, the chosen samples in the Nyström method are all assumed to be of equal importance, which deviates from the integral equation that defines the kernel eigenfunctions. Motivated by this observation, we extend the Nyström method to a(More)
Practical data mining rarely falls exactly into the supervised learning scenario. Rather, the growing amount of unlabeled data poses a big challenge to large-scale semi-supervised learning (SSL). We note that the computational intensiveness of graph-based SSL arises largely from the manifold or graph regularization, which in turn lead to large models that(More)
Kernel Support Vector Machine delivers state-of-the-art results in non-linear classification , but the need to maintain a large number of support vectors poses a challenge in large scale training and testing. In contrast , linear SVM is much more scalable even on limited computing recourses (e.g. daily life PCs), but the learned model cannot capture(More)
There are a number of symptoms, both neurological and behavioral, associated with a single episode of r mild traumatic brain injury (mTBI). Neuropsychological testing and conventional neuroimaging techniques are not sufficiently sensitive to detect these changes, which adds to the complexity and difficulty in relating symptoms from mTBI to their underlying(More)
PURPOSE To characterize the disease-causing mutations in four generations of a Chinese family affected with bilateral congenital nuclear and zonular pulverulent cataract. METHODS Detailed family history and clinical data were recorded. The phenotype was documented using slit-lamp photography. Candidate genes were amplified using PCR and screened for(More)
This paper studies the problem of question retrieval in community question answering (CQA). To bridge lexical gaps in questions, which is regarded as the biggest challenge in retrieval, state-of-the-art methods learn translation models using answers under an assumption that they are parallel texts. In practice, however, questions and answers are far from(More)