We study semi-supervised learning when the data consists of multiple intersecting manifolds. We give a finite sample analysis to quantify the potential gain of using unlabeled data in this multi-manifold setting. We then propose a semi-supervised learning algorithm that separates different manifolds into decision sets, and performs supervised learning within each set. Our algorithm involves a n...

Ordinal regression is an important research topic in machine learning. It aims to automatically determine the implied rating of a data item on a fixed, discrete rating scale. In this paper, we present a novel ordinal regression approach via manifold learning, which is capable of uncovering the embedded nonlinear structure of the data set according to the observations in the highdimensional feat...

We present an interactive learning method that enables a user to iteratively refine a regression model. The user examines the output of the model, visualized as the vertical axis of a 2D scatterplot, and provides corrections by repositioning individual data instances to the correct output level. Each repositioned data instance acts as a control point for altering the learned model, using the ge...

Multi-task learning (MTL) has drawn a lot of attentions in machine learning. By training multiple tasks simultaneously, information can be better shared across tasks. This leads to significant performance improvement in many problems. However, most existing methods assume that all tasks are related or their relationship follows a simple and specified structure. In this paper, we propose a novel...

In this paper, vector field learning is proposed as a new application of manifold learning to vector field. We also provide a learning framework to extract significant features from vector data. Vector data containing position, direction and magnitude information is different from common point data only containing position information. The algorithm of locally linear embedding (LLE) is extended...

Manifold learning of medical images plays a potentially important role for modeling anatomical variability within a population with pplications that include segmentation, registration, and prediction of clinical parameters. This paper describes a novel method for learning the manifold of 3D brain images that, unlike most existing manifold learning methods, does not require the manifold space to...

We address the task of fusing ranked lists of documents that are retrieved in response to a query. Past work on this task of rank aggregation often assumes that documents in the lists being fused are independent and that only the documents that are ranked high in many lists are likely to be relevant to a given topic. We propose manifold learning aggregation approaches, ManX and v-ManX, that bui...

In many imaging applications such as Computed Tomography (CT) in medical imaging and Synthetic Aperture Radar (SAR) imaging, the collected raw data, residing in R , of the receiver or detector can be modeled as data lying in the Fourier space of the target reflectivity function. The magnitude of the reflectivity is considered as the image of the target, and we are often interested in detecting ...

Collective matrix factorization has achieved a remarkable success in document classification in the literature of transfer learning. However, the learned latent factors still suffer from the divergence between different domains and thus are usually not discriminative for an appropriate assignment of category labels. Based on these observations, we impose a discriminative regression model over t...

Manifold learning has recently gained a lot of interest by machine learning practitioners. Here we provide a mathematically rigorous treatment of some of the techniques in unsupervised learning in context of manifolds. We will study the problems of dimension reduction and density estimation and present some recent results in terms of fast convergence rates when the data lie on a manifold.