5709930
Document clustering using locality preserving indexing
We propose a novel document clustering method which aims to cluster the documents into different semantic classes. The document space is generally of high dimensionality and clustering in such a high dimensional space is often infeasible due to the curse of dimensionality. By using locality preserving indexing (LPI), the documents can be projected into a lower-dimensional semantic space in which the documents related to the same semantics are close to each other. Different from previous document clustering methods based on latent semantic indexing (LSI) or nonnegative matrix factorization (NMF), our method tries to discover both the geometric and discriminating structures of the document space. Theoretical analysis of our method shows that LPI is an unsupervised approximation of the supervised linear discriminant analysis (LDA) method, which gives the intuitive motivation of our method. Extensive experimental evaluations are performed on the Reuters-21578 and TDT2 data sets.
6559152
Tensor space model for document analysis
Vector Space Model (VSM) has been at the core of information retrieval for the past decades. VSM considers the documents as vectors in high dimensional space.In such a vector space, techniques like Latent Semantic Indexing (LSI), Support Vector Machines (SVM), Naive Bayes, etc., can be then applied for indexing and classification. However, in some cases, the dimensionality of the document space might be extremely large, which makes these techniques infeasible due to the curse of dimensionality. In this paper, we propose a novel Tensor Space Model for document analysis. We represent documents as the second order tensors, or matrices. Correspondingly, a novel indexing algorithm called Tensor Latent Semantic Indexing (TensorLSI) is developed in the tensor space. Our theoretical analysis shows that TensorLSI is much more computationally efficient than the conventional Latent Semantic Indexing, which makes it applicable for extremely large scale data set. Several experimental results on standard document data sets demonstrate the efficiency and effectiveness of our algorithm.
3132633
Tensor Subspace Analysis
Previous work has demonstrated that the image variations of many objects (human faces in particular) under variable lighting can be effectively modeled by low dimensional linear spaces. The typical linear sub-space learning algorithms include Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Locality Preserving Projection (LPP). All of these methods consider an n1 x n2 image as a high dimensional vector in ℝn1 x n2, while an image represented in the plane is intrinsically a matrix. In this paper, we propose a new algorithm called Tensor Subspace Analysis (TSA). TSA considers an image as the second order tensor in Rn1 ⊗ Rn2, where Rn1 and Rn2 are two vector spaces. The relationship between the column vectors of the image matrix and that between the row vectors can be naturally characterized by TSA. TSA detects the intrinsic local geometrical structure of the tensor space by learning a lower dimensional tensor subspace. We compare our proposed approach with PCA, LDA and LPP methods on two standard databases. Experimental results demonstrate that TSA achieves better recognition rate, while being much more efficient.
1623769
Orthogonal locality preserving indexing
We consider the problem of document indexing and representation. Recently, Locality Preserving Indexing (LPI) was proposed for learning a compact document subspace. Different from Latent Semantic Indexing which is optimal in the sense of global Euclidean structure, LPI is optimal in the sense of local manifold structure. However, LPI is extremely sensitive to the number of dimensions. This makes it difficult to estimate the intrinsic dimensionality, while inaccurately estimated dimensionality would drastically degrade its performance. One reason leading to this problem is that LPI is non-orthogonal. Non-orthogonality distorts the metric structure of the document space. In this paper, we propose a new algorithm called Orthogonal LPI. Orthogonal LPI iteratively computes the mutually orthogonal basis functions which respect the local geometrical structure. Moreover, our empirical study shows that OLPI can have more locality preserving power than LPI. We compare the new algorithm to LSI and LPI. Extensive experimental results show that Orthogonal LPI obtains better performance than both LSI and LPI. More crucially, it is insensitive to the number of dimensions, which makes it an efficient data preprocessing method for text clustering, classification, retrieval, etc.
12494221
Statistical and computational analysis of locality preserving projection
Recently, several manifold learning algorithms have been proposed, such as ISOMAP (Tenenbaum et al., 2000), Locally Linear Embedding (Roweis & Saul, 2000), Laplacian Eigenmap (Belkin & Niyogi, 2001), Locality Preserving Projection (LPP) (He & Niyogi, 2003), etc. All of them aim at discovering the meaningful low dimensional structure of the data space. In this paper, we present a statistical analysis of the LPP algorithm. Different from Principal Component Analysis (PCA) which obtains a subspace spanned by the largest eigenvectors of the global covariance matrix, we show that LPP obtains a subspace spanned by the smallest eigenvectors of the local covariance matrix. We applied PCA and LPP to real world document clustering task. Experimental results show that the performance can be significantly improved in the subspace, and especially LPP works much better than PCA.
14516443
Learning a semantic space from user's relevance feedback for image retrieval
As current methods for content-based retrieval are incapable of capturing the semantics of images, we experiment with using spectral methods to infer a semantic space from user's relevance feedback, so that our system will gradually improve its retrieval performance through accumulated user interactions. In addition to the long-term learning process, we also model the traditional approaches to query refinement using relevance feedback as a short-term learning process. The proposed short- and long-term learning frameworks have been integrated into an image retrieval system. Experimental results on a large collection of images have shown the effectiveness and robustness of our proposed algorithms.
31879969
A Method for Constructing Algebraic Petri Nets
Algebraic Petri nets are a powerful formal method for specifying concurrent and distributed systems. We present a new method of constructing algebraic Petri net specifications by establishing a relationship between algebraic Petri nets with structured analysis methods. Algebraic Petri net specifications are systematically derived from data flow diagrams, a data dictionary, and decision table process specifications. Our results facilitate the application of algebraic Petri nets and also provide a potential analysis technique for informal specifications written in structured analysis methods.
28830107
Introducing software architecture specification and analysis in SAM through an example
Abstract Software architecture study has become one of the most active research areas in software engineering in the recent years. Although there have been many published results on specification and analysis method of software architectures, information on sound systematic methodology for modeling and analyzing software architectures is lacking. In this article, we present a formal systematic software architecture specification and analysis methodology called SAM and show how to apply SAM to specify a command control (C2) system and to analyze its real-time constraints.
25659954
An Improved Algorithm for the Planar 3-Cut Problem
Abstract A 3-cut of a connected graph G is a subset of edges which, when deleted, separates G into three connected components. In this paper we present an O ( n log n ) algorithm for finding a minimum 3-cut in planar graphs. Our algorithm improves the best previously known algorithm for the problem by an O( n log n) factor.
20141160
A method for analyzing properties of hierarchical predicate transition nets
Hierarchical high level Petri nets have been proposed in recent years as a powerful formal method for modeling large concurrent and distributed systems but they are even more difficult to analyze than flat high level Petri nets, which are also lacking effective analysis methods themselves. A method for analyzing properties of hierarchical predicate transition Petri nets is proposed. The method employs two temporal induction techniques, one for safety properties and the other for liveness properties, without using temporal logic formalism. Within each induction technique, a hybrid reasoning technique combining net structural and behavioral reasoning, and ordinary first order logic reasoning is used.
14477095
Learning and Incorporating Top-Down Cues in Image Segmentation
Bottom-up approaches, which rely mainly on continuity principles, are often insufficient to form accurate segments in natural images. In order to improve performance, recent methods have begun to incorporate top-down cues, or object information, into segmentation. In this paper, we propose an approach to utilizing category-based information in segmentation, through a formulation as an image labelling problem. Our approach exploits bottom-up image cues to create an over-segmented representation of an image. The segments are then merged by assigning labels that correspond to the object category. The model is trained on a database of images, and is designed to be modular: it learns a number of image contexts, which simplify training and extend the range of object classes and image database size that the system can handle. The learning method estimates model parameters by maximizing a lower bound of the data likelihood. We examine performance on three real-world image databases, and compare our system to a standard classifier and other conditional random field approaches, as well as a bottom-up segmentation method.