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.
10726702
Locality Preserving Projections
Many problems in information processing involve some form of dimensionality reduction. In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis (PCA) – a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold. As a result, LPP shares many of the data representation properties of nonlinear techniques such as Laplacian Eigenmaps or Locally Linear Embedding. Yet LPP is linear and more crucially is defined everywhere in ambient space rather than just on the training data points. This is borne out by illustrative examples on some high dimensional data sets.
14585493
Learning a locality preserving subspace for visual recognition
We have demonstrated that the face recognition performance can be improved significantly in low dimensional linear subspaces. Conventionally, principal component analysis (PCA) and linear discriminant analysis (LDA) are considered effective in deriving such a face subspace. However, both of them effectively see only the Euclidean structure of face space. We propose a new approach to mapping face images into a subspace obtained by locality preserving projections (LPP) for face analysis. We call this Laplacianface approach. Different from PCA and LDA, LPP finds an embedding that preserves local information, and obtains a face space that best detects the essential manifold structure. In this way, the unwanted variations resulting from changes in lighting, facial expression, and pose may be eliminated or reduced. We compare the proposed Laplacianface approach with eigenface and fisherface methods on three test datasets. Experimental results show that the proposed Laplacianface approach provides a better representation and achieves lower error rates in face recognition.
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.
9650912
Learning an image manifold for retrieval
We consider the problem of learning a mapping function from low-level feature space to high-level semantic space. Under the assumption that the data lie on a submanifold embedded in a high dimensional Euclidean space, we propose a relevance feedback scheme which is naturally conducted only on the image manifold in question rather than the total ambient space. While images are typically represented by feature vectors in Rn, the natural distance is often different from the distance induced by the ambient space Rn. The geodesic distances on manifold are used to measure the similarities between images. However, when the number of data points is small, it is hard to discover the intrinsic manifold structure. Based on user interactions in a relevance feedback driven query-by-example system, the intrinsic similarities between images can be accurately estimated. We then develop an algorithmic framework to approximate the optimal mapping function by a Radial Basis Function (RBF) neural network. The semantics of a new image can be inferred by the RBF neural network. Experimental results show that our approach is effective in improving the performance of content-based image retrieval systems.
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.
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.
20004613
Disk Embeddings of Planar Graphs
Abstract 
Given a planar graph $G=(V,E)$ and a rooted forest ${\FF}=(V_{\FF}, A_{\FF})$ 
with leaf set $V$, we wish to decide whether $G$ has a plane embedding $\GG$ 
satisfying the following condition: There are $|V_{\FF}|-|V|$ pairwise noncrossing 
Jordan curves in the plane one-to-one corresponding to the nonleaf vertices of 
${\FF}$ such that for every nonleaf vertex $f$ of ${\FF}$, the interior of the curve 
$\JJ_f$ corresponding to $f$ contains all the leaf descendants of $f$ in ${\FF}$
but contains no other leaves of ${\FF}$. 
This problem arises from theoretical studies in geographic database systems. 
It is unknown whether this problem can be solved in polynomial time. 
This paper presents an almost linear-time algorithm for a nontrivial special case 
where the set of leaf descendants of each nonleaf vertex $f$ in ${\FF}$ induces 
a connected subgraph of $G$. 


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.
16128617
CyberSeer: 3D audio-visual immersion for network security and management
Large complex networks have become an inseparable part of modern society. However, very little has been done to develop tools to manage and ensure the security of such networks. Network operators continue to slave over endless daily logs and alerts in a struggle to keep networks operational. Perhaps the most formidable enemy of network operations today is the volume of management data that must be perused. Expensive commercial products attempt to visualize data but with limited utility, as witnessed by the prevailing use of command-line interfaces and homegrown scripts. In addition to data collection tools, operators need to immediately observe and debug the effects of their actions; yet that information is buried deep in the data that pours daily from monitoring equipment. Thus, they need better ways to abstract network events and better, more informative ways to render them.
 In this work we first propose a new approach for abstracting network information, namely spectral representation. Second, we introduce immersive spatial audio representations of network events. Third, we introduce 3D interactive auto-stereoscopic (AS) displays for visual representations. We integrate the three techniques as follows. We use spectral techniques to extract complex events buried inside voluminous network traces and logs. Then, we create a desktop interactive immersive auto-stereoscopic 3D environment that is seamlessly integrated with multi-channel spatially rendered audio to render such events in a far more human-friendly fashion.
30190247
A Fast General Methodology for Information-Theoretically Optimal Encodings of Graphs
We propose a fast methodology for encoding graphs with information-theoretically minimum numbers of bits. Specifically, a graph with property $\pi$ is called a {\em $\pi$-graph}. If $\pi$ satisfies certain properties, then an n-node m-edge $\pi$-graph G can be encoded by a binary string X such that (1) G and X can be obtained from each other in O(n log n) time, and (2) X has at most $\beta(n)+o(\beta(n))$ bits for any continuous superadditive function $\beta(n)$ so that there are at most $2^{\beta(n)+o(\beta(n))}$ distinct $n$-node $\pi$-graphs. The methodology is applicable to general classes of graphs; this paper focuses on planar graphs. Examples of such $\pi$ include all conjunctions over the following groups of properties: (1) G is a planar graph or a plane graph; (2) $G$ is directed or undirected; (3) $G$ is triangulated, triconnected, biconnected, merely connected, or not required to be connected; (4) the nodes of G are labeled with labels from $\{1,\ldots, \ell_1\}$ for $\ell_1\leq n$; (5) the edges of G are labeled with labels from $\{1,\ldots, \ell_2\}$ for $\ell_2\leq m$; and (6) each node (respectively, edge) of G has at most $\ell_3=O(1)$ self-loops (respectively, $\ell_4=O(1)$ multiple edges). Moreover, $\ell_3$ and $\ell_4$ are not required to be O(1) for the cases of $\pi$ being a plane triangulation. These examples are novel applications of small cycle separators of planar graphs and are the only nontrivial classes of graphs, other than rooted trees, with known polynomial-time information-theoretically optimal coding schemes.