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  • Efficient Manifold Ranking for Image Retrieval

    Bin Xu1, Jiajun Bu1, Chun Chen1, Deng Cai2, Xiaofei He2, Wei Liu3, Jiebo Luo41Zhejiang Provincial Key Laboratory of Service Robot

    College of Computer Science, Zhejiang University, Hangzhou, China{xbzju,bjj,chenc,hezhanying}@zju.edu.cn

    2State Key Lab of CAD&CG, College of Computer Science, Zhejiang University, Hangzhou, China{dengcai,xiaofeihe}@cad.zju.edu.cn

    3Columbia University, New York, NY, USA, wliu@ee.columbia.edu4Kodak Research Laboratories, Eastman Kodak Company, Rochester, NY, USA, jiebo.luo@kodak.com

    ABSTRACTManifold Ranking (MR), a graph-based ranking algorithm,has been widely applied in information retrieval and shownto have excellent performance and feasibility on a varietyof data types. Particularly, it has been successfully appliedto content-based image retrieval, because of its outstandingability to discover underlying geometrical structure of thegiven image database. However, manifold ranking is com-putationally very expensive, both in graph construction andranking computation stages, which significantly limits its ap-plicability to very large data sets. In this paper, we extendthe original manifold ranking algorithm and propose a newframework named Efficient Manifold Ranking (EMR). Weaim to address the shortcomings of MR from two perspec-tives: scalable graph construction and efficient computation.Specifically, we build an anchor graph on the data set insteadof the traditional k-nearest neighbor graph, and design a newform of adjacency matrix utilized to speed up the rankingcomputation. The experimental results on a real world im-age database demonstrate the effectiveness and efficiency ofour proposed method. With a comparable performance tothe original manifold ranking, our method significantly re-duces the computational time, makes it a promising methodto large scale real world retrieval problems.

    Categories and Subject DescriptorsH.3.3 [Information Search and Retrieval]: Retrievalmodels; H.2.8 [Database Applications]: Image databases

    General TermsAlgorithm, Performance

    KeywordsEfficient manifold ranking, image retrieval, graph-based al-gorithm, out-of-sample

    Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.SIGIR11 July 2428, 2011, Beijing, ChinaCopyright 2011 ACM 978-1-4503-0757-4/11/07 ...$10.00.

    1. INTRODUCTIONTraditional image retrieval systems are based on keyword

    search, such as Google and Yahoo image search. In thesesystems, user keyword is matched with the context aroundan image including the title, manual annotation, web doc-ument, etc. These systems dont utilize information fromimages. However these systems suffer many problems, suchas shortage of the text information and inconsistency of themeaning of the text and image.

    Content-based image retrieval (CBIR) is a considerablechoice to overcome these difficulties. CBIR has drawed agreat attention in the past two decades [5, 19, 27]. Differ-ent from traditional keyword search systems, CBIR systemsutilize the low-level features (color, texture, shape, etc.),automatically extracted from images. This is a vital char-acter for efficient management and search in a large imagedatabase. But the low-level features used in CBIR systemsare often visually characterized, and with no direct connec-tion with semantic concepts of the images. How to narrowthe semantic gap has been the main challenge for CBIR.

    Many data sets have underlying cluster or manifold struc-ture. Under such circumstances, the assumption of label con-sistency is reasonable [23, 36]. It means that those nearbydata points, or points belong to the same cluster or mani-fold, are very likely to share the same semantic label. Thisphenomenon is extremely important to explore the seman-tic relevance when the label information is unknown. Thus,a good CBIR method should consider low-level features aswell as intrinsic structure of the data.

    Manifold Ranking (MR) [36,37], a semi-supervised graph-based ranking algorithm, has been widely applied in infor-mation retrieval, and shown to have excellent performanceand feasibility on a variety of data types, such as the text[28], image [9], and video [34]. The core idea of manifoldranking is to rank the data with respect to the intrinsicstructure collectively revealed by a large number of data.By taking the underlying structure into account, manifoldranking assigns each data point a relative ranking score, in-stead of an absolute pairwise similarity as traditional ways.The score is treated as a distance metric defined on the man-ifold, which is more meaningful to capturing the semanticrelevance degree. He et al. [9] firstly applied manifold rank-ing to CBIR, and significantly improved image retrieval per-formance compared with state-of-the-art algorithms.

    However, manifold ranking has its own drawbacks to han-dle large scale data sets it has expensive computational

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  • cost, both in graph construction and ranking computationstages. Particularly, it is costly to handle an out-of-samplequery (a new sample). That means original manifold rank-ing is inadequate for a real world CBIR system, in whichthe user provided query is always an out-of-sample. Its in-tolerable for a user to wait a long time to get returns.

    In this paper, we extend the original manifold ranking andpropose a novel framework named Efficient Manifold Rank-ing (EMR). We try to address the shortcomings of manifoldranking from two perspectives: the first is scalable graphconstruction; and the second is efficient computation, espe-cially for out-of-sample retrieval. The main contributions ofthis paper are as follows. (1) Based on the anchor graphconstruction [18,35], we design a new form of adjacency ma-trix and give it an intuitive explanation. (2) By the newform, our method EMR achieves a comparable performanceto original manifold ranking but significantly reduces thecomputational time.

    The rest of this paper is organized as follows. In section2, we briefly discuss some related works and in section 3, wereview the manifold ranking algorithm and make a detailedanalysis. The proposed approach EMR is described in sec-tion 4. In section 5, we present the experiment results on areal world image database. Finally we provide an extensionanalysis in section 6 and conclusions in section 7.

    2. RELATED WORKIn this section, we discuss two most relevant topics to our

    work: ranking model and content-based image retrieval.The problem of ranking has recently gained great atten-

    tions in both information retrieval and machine learningareas. Conventional ranking models can be content basedmodels, like the Vector Space Model, BM25, and the lan-guage modeling [22]; or link structure based models, like thefamous PageRank [2] and HITS [15]; or cross media mod-els [13]. Another important category is the learning to rankmodel, which aims to optimize a ranking function that incor-porates relevance features and avoids tuning a large numberof parameters empirically [7, 26]. However, many conven-tional models ignore the important issue of efficiency, whichis crucial for a real-time systems, such as a web application.In [29], the authors present a unified framework for jointlyoptimizing effectiveness and efficiency.

    2.1 Graph-based RankingIn this paper, we focus on a particular kind of ranking

    model graph-based ranking. It has been successfully ap-plied in link-structure analysis of the web [2, 15] and socialnetworks research [3, 8, 17]. Generally, a graph can be de-noted as G = (V,E,W ), where V is a set of vertices in whicheach vertex represents a data point, E V V is a set ofedges connecting related vertices, and W is a adjacency ma-trix recording the pairwise weights between vertices. Theobject of a graph-based ranking model is to decide the im-portance of a vertex in a graph, based on local or globalinformation draw from the graph.

    Agarwal [1] proposed to model the data by a weightedgraph, and incorporated this graph structure into the rank-ing function as a regularizer. Guan et al. [8] proposed agraph-based ranking algorithm for interrelated multi-typeresources to generate personalized tag recommendation. Liuet al. [17] proposed an automatically tag ranking scheme byperforming a random walk over a tag similarity graph. In [3],

    the authors made the music recommendation by ranking ona unified hypergraph, combining with rich social informationand music content. Recently, there have been some paperson speeding up manifold ranking. In [11], the authors parti-tioned the data into several parts and computed the rankingfunction by a block-wise way.

    2.2 Content-based Image RetrievalIn many cases, we have no more information than the data

    itself. Without label information, capturing semantic rela-tionship between images is quite difficult. A great amount ofresearches have been performed for designing more informa-tive low-level features (e.g., SIFT features [20]) to representimages, or better metrics (e.g., DPF [16]) to measure theperceptual similarity, but their performance is restricted bymany conditions and is sensitive to the data. Relevancefeedback [24] is a powerful tool for interactive CBIR. Usershigh level perception is captured by dynamically updatedweights based on the users feedback.

    Many traditional image retrieval methods focus on thedata features too much, and they ignore the underlyingstructure information, which is of great importance for se-mantic discovery, especially when the label information isunknow