Jiayuan Huang

Learning from labeled and unlabeled data on a directed graph

We propose a general framework for learning from labeled and unlabeled data on a directed graph in which the structure of the graph including the directionality of the edges is considered. The time complexity of the algorithm derived from this framework is nearly linear due to recently developed numerical techniques. In the absence of labeled instances, this framework can be utilized as a spectral clustering method for directed graphs, which generalizes the spectral clustering approach for undirected graphs. We have applied our framework to real-world web classification problems and obtained encouraging results.

Web communities identification from random walks

We propose a technique for identifying latent Web communities based solely on the hyperlink structure of the WWW, via random walks. Although the topology of the Directed Web Graph encodes important information about the content of individual Web pages, it also reveals useful meta-level information about user communities. Random walk models are capable of propagating local link information throughout the Web Graph, which can be used to reveal hidden global relationships between different regions of the graph. Variations of these random walk models are shown to be effective at identifying latent Web communities and revealing link topology. To efficiently extract these communities from the stationary distribution defined by a random walk, we exploit a computationally efficient form of directed spectral clustering. The performance of our approach is evaluated in real Web applications, where the method is shown to effectively identify latent Web communities based on link topology only.

Tangent-corrected embedding

Images and other high-dimensional data can frequently be characterized by a low dimensional manifold (e.g. one that corresponds to the degrees of freedom of the camera). Recently, nonlinear manifold learning techniques have been used to map images to points in a lower dimension space, capturing some of the dynamics of the camera or the subjects. In general, these methods do not take advantage of any prior understanding of the dynamics we might have, relying instead on local Euclidean distances that can be misleading in image space. In practice, we frequently have some prior knowledge regarding the transformations that relate images (e.g. rotation, translation, etc). We present a method for augmenting existing embedding techniques with additional information derived from known transformations, either in the form of tangent spaces that locally characterize the manifold or distances derived from reconstruction errors. The extra information is incorporated directly into the cost function of the embedding technique. The techniques we augment are largely attractive because there is a closed form solution for their cost optimization. Our approach likewise produces a closed form solution for the augmented cost function. Experiments demonstrate the effectiveness of the approach on a variety of image data.

Transformation-Invariant Embedding for Image Analysis

Dimensionality reduction is an essential aspect of visual processing. Traditionally, linear dimensionality reduction techniques such as principle components analysis have been used to find low dimensional linear subspaces in visual data. However, sub-manifolds in natural data are rarely linear, and consequently many recent techniques have been developed for discovering non-linear manifolds. Prominent among these are Local Linear Embedding and Isomap. Unfortunately, such techniques currently use a naive appearance model that judges image similarity based solely on Euclidean distance. In visual data, Euclidean distances rarely correspond to a meaningful perceptual difference between nearby images. In this paper, we attempt to improve the quality of manifold inference techniques for visual data by modeling local neighborhoods in terms of natural transformations between images—for example, by allowing image operations that extend simple differences and linear combinations. We introduce the idea of modeling local tangent spaces of the manifold in terms of these richer transformations. Given a local tangent space representation, we then embed data in a lower dimensional coordinate system while preserving reconstruction weights. This leads to improved manifold discovery in natural image sets.