16394993
Regularization on Discrete Spaces
We consider the classification problem on a finite set of objects. Some of them are labeled, and the task is to predict the labels of the remaining unlabeled ones. Such an estimation problem is generally referred to as transductive inference. It is well-known that many meaningful inductive or supervised methods can be derived from a regularization framework, which minimizes a loss function plus a regularization term. In the same spirit, we propose a general discrete regularization framework defined on finite object sets, which can be thought of as discrete analogue of classical regularization theory. A family of transductive inference schemes is then systemically derived from the framework, including our earlier algorithm for transductive inference, with which we obtained encouraging results on many practical classification problems. The discrete regularization framework is built on discrete analysis and geometry developed by ourselves, in which a number of discrete differential operators of various orders are constructed, which can be thought of as discrete analogues of their counterparts in the continuous case.
8020389
Learning from Labeled and Unlabeled Data Using Random Walks
We consider the general problem of learning from labeled and unlabeled data. Given a set of points, some of them are labeled, and the remaining points are unlabeled. The goal is to predict the labels of the unlabeled points. Any supervised learning algorithm can be applied to this problem, for instance, Support Vector Machines (SVMs). The problem of our interest is if we can implement a classifier which uses the unlabeled data information in some way and has higher accuracy than the classifiers which use the labeled data only. Recently we proposed a simple algorithm, which can substantially benefit from large amounts of unlabeled data and demonstrates clear superiority to supervised learning methods. Here we further investigate the algorithm using random walks and spectral graph theory, which shed light on the key steps in this algorithm.
16721854
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.
13800566
Multi-task text segmentation and alignment based on weighted mutual information
Text segmentation is important for text analysis, while text alignment is to determine shared sub-topics among similar documents. Multi-task text segmentation and alignment is the extension of single-task segmentation to utilize information of multi-source documents. In this paper we introduce a novel domain-independent unsupervised method for multi-task segmentation and alignment based on the idea that the optimal segmentation and alignment maximizes weighted mutual information, mutual information with term weights. The experiment results show that our approach works well.
474823
Boosting the Feature Space: Text Classification for Unstructured Data on the Web
The issue of seeking efficient and effective methods for classifying unstructured text in large document corpora has received much attention in recent years. Traditional document representation like bag-of-words encodes documents as feature vectors, which usually leads to sparse feature spaces with large dimensionality, thus making it hard to achieve high classification accuracies. This paper addresses the problem of classifying unstructured documents on the Web. A classification approach is proposed that utilizes traditional feature reduction techniques along with a collaborative filtering method for augmenting document feature spaces. The method produces feature spaces with an order of magnitude less features compared with a baseline bag-of-words feature selection method. Experiments on both real-world data and benchmark corpus indicate that our approach improves classification accuracy over the traditional methods for both support vector machines and AdaBoost classifiers.
13242297
A clustering method for web data with multi-type interrelated components
Traditional clustering algorithms work on "flat" data, making the assumption that the data instances can only be represented by a set of homogeneous and uniform features. Many real world data, however, is heterogeneous in nature, comprising of multiple types of interrelated components. We present a clustering algorithm, K-SVMeans, that integrates the well known K-Means clustering with the highly popular Support Vector Machines(SVM) in order to utilize the richness of data. Our experimental results on authorship analysis of scientific publications show that K-SVMeans achieves better clustering performance than homogeneous data clustering.
12261862
Capacity of reproducing kernel spaces in learning theory
The capacity of reproducing kernel Hilbert spaces (RKHS) plays an essential role in the analysis of learning theory. Covering numbers and packing numbers of balls of these reproducing kernel spaces are important measurements of this capacity. We first present lower bound estimates for the packing numbers by means of nodal functions. Then we show that if a Mercer kernel is C/sup s/ (for some s>0 being not an even integer), the RKHS associated with this kernel can be embedded into C/sup s/2/. This gives upper-bound estimates for the covering number concerning Sobolev smooth kernels.Examples and applications to V/sub /spl gamma// dimension and Tikhonov (1977) regularization are presented to illustrate the upper- and lower-bound estimates.
7316344
CLINCH: Clustering Incomplete High-Dimensional Data for Data Mining Application
Clustering is a common technique in data mining to discover hidden patterns from massive datasets. With the development of privacy-maintaining data mining application, clustering incomplete high-dimensional data has becoming more and more useful. Motivated by these limits, we develop a novel algorithm CLINCH, which could produce fine clusters on incomplete high-dimensional data space. To handle missing attributes, CLINCH employs a prediction method that can be more precise than traditional techniques. On the other hand, we also introduce an efficient way in which dimensions are processed one by one to attack the “curse of dimensionality”. Experiments show that our algorithm not only outperforms many existing high-dimensional clustering algorithms in scalability and efficiency, but also produces precise results.