Benyu Zhang

Graph Embedding and Extensions: A General Framework for Dimensionality Reduction

A large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called marginal Fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions

Graph embedding: a general framework for dimensionality reduction

In the last decades, a large family of algorithms - supervised or unsupervised; stemming from statistic or geometry theory - have been proposed to provide different solutions to the problem of dimensionality reduction. In this paper, beyond the different motivations of these algorithms, we propose a general framework, graph embedding along with its linearization and kernelization, which in theory reveals the underlying objective shared by most previous algorithms. It presents a unified perspective to understand these algorithms; that is, each algorithm can be considered as the direct graph embedding or its linear/kernel extension of some specific graph characterizing certain statistic or geometry property of a data set. Furthermore, this framework is a general platform to develop new algorithm for dimensionality reduction. To this end, we propose a new supervised algorithm, Marginal Fisher Analysis (MFA), for dimensionality reduction by designing two graphs that characterize the intra-class compactness and inter-class separability, respectively. MFA measures the intra-class compactness with the distance between each data point and its neighboring points of the same class, and measures the inter-class separability with the class margins; thus it overcomes the limitations of traditional Linear Discriminant Analysis algorithm in terms of data distribution assumptions and available projection directions. The toy problem on artificial data and the real face recognition experiments both show the superiority of our proposed MFA in comparison to LDA.

Improving web search results using affinity graph

In this paper, we propose a novel ranking scheme named Affinity Ranking (AR) to re-rank search results by optimizing two metrics: (1) diversity -- which indicates the variance of topics in a group of documents; (2) information richness -- which measures the coverage of a single document to its topic. Both of the two metrics are calculated from a directed link graph named Affinity Graph (AG). AG models the structure of a group of documents based on the asymmetric content similarities between each pair of documents. Experimental results in Yahoo! Directory, ODP Data, and Newsgroup data demonstrate that our proposed ranking algorithm significantly improves the search performance. Specifically, the algorithm achieves 31% improvement in diversity and 12% improvement in information richness relatively within the top 10 search results.

Privacy-enhancing personalized web search

Personalized web search is a promising way to improve search quality by customizing search results for people with individual information goals. However, users are uncomfortable with exposing private preference information to search engines. On the other hand, privacy is not absolute, and often can be compromised if there is a gain in service or profitability to the user. Thus, a balance must be struck between search quality and privacy protection. This paper presents a scalable way for users to automatically build rich user profiles. These profiles summarize a user.s interests into a hierarchical organization according to specific interests. Two parameters for specifying privacy requirements are proposed to help the user to choose the content and degree of detail of the profile information that is exposed to the search engine. Experiments showed that the user profile improved search quality when compared to standard MSN rankings. More importantly, results verified our hypothesis that a significant improvement on search quality can be achieved by only sharing some higher-level user profile information, which is potentially less sensitive than detailed personal information.

Web-page classification through summarization

Web-page classification is much more difficult than pure-text classification due to a large variety of noisy information embedded in Web pages. In this paper, we propose a new Web-page classification algorithm based on Web summarization for improving the accuracy. We first give empirical evidence that ideal Web-page summaries generated by human editors can indeed improve the performance of Web-page classification algorithms. We then propose a new Web summarization-based classification algorithm and evaluate it along with several other state-of-the-art text summarization algorithms on the LookSmart Web directory. Experimental results show that our proposed summarization-based classification algorithm achieves an approximately 8.8% improvement as compared to pure-text-based classification algorithm. We further introduce an ensemble classifier using the improved summarization algorithm and show that it achieves about 12.9% improvement over pure-text based methods.

Effective and efficient dimensionality reduction for large-scale and streaming data preprocessing

Dimensionality reduction is an essential data preprocessing technique for large-scale and streaming data classification tasks. It can be used to improve both the efficiency and the effectiveness of classifiers. Traditional dimensionality reduction approaches fall into two categories: feature extraction and feature selection. Techniques in the feature extraction category are typically more effective than those in feature selection category. However, they may break down when processing large-scale data sets or data streams due to their high computational complexities. Similarly, the solutions provided by the feature selection approaches are mostly solved by greedy strategies and, hence, are not ensured to be optimal according to optimized criteria. In this paper, we give an overview of the popularly used feature extraction and selection algorithms under a unified framework. Moreover, we propose two novel dimensionality reduction algorithms based on the orthogonal centroid algorithm (OC). The first is an incremental OC (IOC) algorithm for feature extraction. The second algorithm is an orthogonal centroid feature selection (OCFS) method which can provide optimal solutions according to the OC criterion. Both are designed under the same optimization criterion. Experiments on Reuters Corpus Volume-1 data set and some public large-scale text data sets indicate that the two algorithms are favorable in terms of their effectiveness and efficiency when compared with other state-of-the-art algorithms.

SimFusion: measuring similarity using unified relationship matrix

In this paper we use a Unified Relationship Matrix (URM) to represent a set of heterogeneous data objects (e.g., web pages, queries) and their interrelationships (e.g., hyperlinks, user click-through sequences). We claim that iterative computations over the URM can help overcome the data sparseness problem and detect latent relationships among heterogeneous data objects, thus, can improve the quality of information applications that require com- bination of information from heterogeneous sources. To support our claim, we present a unified similarity-calculating algorithm, SimFusion. By iteratively computing over the URM, SimFusion can effectively integrate relationships from heterogeneous sources when measuring the similarity of two data objects. Experiments based on a web search engine query log and a web page collection demonstrate that SimFusion can improve similarity measurement of web objects over both traditional content based algorithms and the cutting edge SimRank algorithm.

OCFS: optimal orthogonal centroid feature selection for text categorization

Text categorization is an important research area in many Information Retrieval (IR) applications. To save the storage space and computation time in text categorization, efficient and effective algorithms for reducing the data before analysis are highly desired. Traditional techniques for this purpose can generally be classified into feature extraction and feature selection. Because of efficiency, the latter is more suitable for text data such as web documents. However, many popular feature selection techniques such as Information Gain (IG) andχ2-test (CHI) are all greedy in nature and thus may not be optimal according to some criterion. Moreover, the performance of these greedy methods may be deteriorated when the reserved data dimension is extremely low. In this paper, we propose an efficient optimal feature selection algorithm by optimizing the objective function of Orthogonal Centroid (OC) subspace learning algorithm in a discrete solution space, called Orthogonal Centroid Feature Selection (OCFS). Experiments on 20 Newsgroups (20NG), Reuters Corpus Volume 1 (RCV1) and Open Directory Project (ODP) data show that OCFS is consistently better than IG and CHI with smaller computation time especially when the reduced dimension is extremely small.

Document Transformation for Multi-label Feature Selection in Text Categorization

Feature selection on multi-label documents for automatic text categorization is an under-explored research area. This paper presents a systematic document transformation framework, whereby the multi-label documents are transformed into single-label documents before applying standard feature selection algorithms, to solve the multi-label feature selection problem. Under this framework, we undertake a comparative study on four intuitive document transformation approaches and propose a novel approach called entropy-based label assignment (ELA), which assigns the labels weights to a multi-label document based on label entropy. Three standard feature selection algorithms are utilized for evaluating the document transformation approaches in order to verify its impact on multi-class text categorization problems. Using a SVM classifier and two multi-label evaluation benchmark text collections, we show that the choice of document transformation approaches can significantly influence the performance of multi-class categorization and that our proposed document transformation approach ELA can achieve better performance than all other approaches.

IMMC: incremental maximum margin criterion

Subspace learning approaches have attracted much attention in academia recently. However, the classical batch algorithms no longer satisfy the applications on streaming data or large-scale data. To meet this desirability, Incremental Principal Component Analysis (IPCA) algorithm has been well established, but it is an unsupervised subspace learning approach and is not optimal for general classification tasks, such as face recognition and Web document categorization. In this paper, we propose an incremental supervised subspace learning algorithm, called Incremental Maximum Margin Criterion (IMMC), to infer an adaptive subspace by optimizing the Maximum Margin Criterion. We also present the proof for convergence of the proposed algorithm. Experimental results on both synthetic dataset and real world datasets show that IMMC converges to the similar subspace as that of batch approach.