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Research Collection School Of Computing and Information Systems

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A Hubel Wiesel Model For Hierarchical Representation Of Concepts In Textual Documents, Kiruthika Ramanathan, Luping Shi, Chong Chong Tow Aug 2010

A Hubel Wiesel Model For Hierarchical Representation Of Concepts In Textual Documents, Kiruthika Ramanathan, Luping Shi, Chong Chong Tow

Research Collection School Of Computing and Information Systems

Hubel Weisel models of the cortex describe visual processing as a hierarchy of increasingly sophisticated representations. While several models exist for image processing, little work has been done with Hubel Weisel models out of the domain of object recognition. In this paper, we describe how such models can be extended to the representation of concepts, resulting in a model that shares several properties with the PDP model of semantic cognition. The model that we propose is also capable of incremental learning, in which the knowledge is stored in the strength of the neuron connections. Degradation of old knowledge occurs as …


Hoare Logic For Graph Programs, Christopher M. Poskitt, Detlef Plump Aug 2010

Hoare Logic For Graph Programs, Christopher M. Poskitt, Detlef Plump

Research Collection School Of Computing and Information Systems

We present a new approach for verifying programs written in GP (for Graph Programs), an experimental programming language for performing computations on graphs at a high level of abstraction. Taking a labelled graph as input, a graph program nondeterministically applies to it a number of graph transformation rules, directed by simple control constructs such as sequential composition and as-long-as-possible iteration. We adapt classical Hoare logic to the domain of graphs, and describe a system of sound proof rules for showing the partial correctness of graph programs.


Cloud Services From A Consumer Perspective, Philip Koehler, Arun Anandasivam, Dan Ma Aug 2010

Cloud Services From A Consumer Perspective, Philip Koehler, Arun Anandasivam, Dan Ma

Research Collection School Of Computing and Information Systems

Although there is an increased attention on Cloud Computing in the academic literature in the recent years, most research work focus on technical aspects of cloud computing. Research on consumers’ preferences for cloud services is limited to studies from consulting and industry companies. This paper fills the gap by empirically identifying consumer preferences for cloud service attributes. Using conjoint methods we reveal the relative importance of different attributes of cloud services. The results help both practitioners and academic researchers to better understand the prerequisites of a successful market introduction of cloud services and to design appropriate services. Moreover, the derived …


Mining Interaction Behaviors For Email Reply Order Prediction, Byung-Won On, Ee Peng Lim, Jing Jiang, Amruta Purandare, Loo Nin Teow Aug 2010

Mining Interaction Behaviors For Email Reply Order Prediction, Byung-Won On, Ee Peng Lim, Jing Jiang, Amruta Purandare, Loo Nin Teow

Research Collection School Of Computing and Information Systems

In email networks, user behaviors affect the way emails are sent and replied. While knowing these user behaviors can help to create more intelligent email services, there has not been much research into mining these behaviors. In this paper, we investigate user engagingness and responsiveness as two interaction behaviors that give us useful insights into how users email one another. Engaging users are those who can effectively solicit responses from other users. Responsive users are those who are willing to respond to other users. By modeling such behaviors, we are able to mine them and to identify engaging or responsive …


Non-Parametric Kernel Ranking Approach For Social Image Retrieval, Jinfeng Zhuang, Steven C. H. Hoi Jul 2010

Non-Parametric Kernel Ranking Approach For Social Image Retrieval, Jinfeng Zhuang, Steven C. H. Hoi

Research Collection School Of Computing and Information Systems

Social image retrieval has become an emerging research challenge in web rich media search. In this paper, we address the research problem of text-based social image retrieval, which aims to identify and return a set of relevant social images that are related to a text-based query from a corpus of social images. Regular approaches for social image retrieval simply adopt typical text-based image retrieval techniques to search for the relevant social images based on the associated tags, which may suffer from noisy tags. In this paper, we present a novel framework for social image re-ranking based on a non-parametric kernel …


Hybrid Time-Frequency Domain Analysis For Inverter-Fed Induction Motor Fault Detection, T. W. Chua, W. W. Tan, Zhaoxia Wang, C. S. Chang Jul 2010

Hybrid Time-Frequency Domain Analysis For Inverter-Fed Induction Motor Fault Detection, T. W. Chua, W. W. Tan, Zhaoxia Wang, C. S. Chang

Research Collection School Of Computing and Information Systems

The detection of faults in an induction motor is important as a part of preventive maintenance. Stator current is one of the most popular signals used for utility-supplied induction motor fault detection as a current sensor can be installed nonintrusively. In variable speeds operation, the use of an inverter to drive the induction motor introduces noise into the stator current so stator current based fault detection techniques become less reliable. This paper presents a hybrid algorithm, which combines time and frequency domain analysis, for broken rotor bar and bearing fault detection. Cluster information obtained by using Independent Component Analysis (ICA) …


Design And Implementation Of A Middleware For Easy Development And Provision Of Stream-Based Services, Seungwoo Kang, Youngki Lee, Sunghwan Ihm, Souneil Park, Su-Myeon Kim, Junehwa Song Jul 2010

Design And Implementation Of A Middleware For Easy Development And Provision Of Stream-Based Services, Seungwoo Kang, Youngki Lee, Sunghwan Ihm, Souneil Park, Su-Myeon Kim, Junehwa Song

Research Collection School Of Computing and Information Systems

This paper proposes MISSA, a novel middleware to facilitate the development and provision of stream-based services in emerging pervasive environments. The stream-based services utilize voluminous and continuously updated data streams as their input. The characteristics of data streams bring new requirements on the development and provision of the services. To satisfy the requirements, a unique service model and a runtime system are designed in MISSA. The key concept of our service model is to separate service logic from handling data streams. This significantly mitigates the burden on service developers by allowing them to only concentrate on the service logic. Job …


Co-Reranking By Mutual Reinforcement For Image Search, Ting Yao, Tao Mei, Chong-Wah Ngo Jul 2010

Co-Reranking By Mutual Reinforcement For Image Search, Ting Yao, Tao Mei, Chong-Wah Ngo

Research Collection School Of Computing and Information Systems

Most existing reranking approaches to image search focus solely on mining “visual” cues within the initial search results. However, the visual information cannot always provide enough guidance to the reranking process. For example, different images with similar appearance may not always present the same relevant information to the query. Observing that multi-modality cues carry complementary relevant information, we propose the idea of co-reranking for image search, by jointly exploring the visual and textual information. Co-reranking couples two random walks, while reinforcing the mutual exchange and propagation of information relevancy across different modalities. The mutual reinforcement is iteratively updated to constrain …


Coherent Bag-Of Audio Words Model For Efficient Large-Scale Video Copy Detection, Yang Liu, Wan-Lei Zhao, Chong-Wah Ngo, Chang-Sheng Xu, Han-Qing Lu Jul 2010

Coherent Bag-Of Audio Words Model For Efficient Large-Scale Video Copy Detection, Yang Liu, Wan-Lei Zhao, Chong-Wah Ngo, Chang-Sheng Xu, Han-Qing Lu

Research Collection School Of Computing and Information Systems

Current content-based video copy detection approaches mostly concentrate on the visual cues and neglect the audio information. In this paper, we attempt to tackle the video copy detection task resorting to audio information, which is equivalently important as well as visual information in multimedia processing. Firstly, inspired by bag-of visual words model, a bag-of audio words (BoA) representation is proposed to characterize each audio frame. Different from naive singlebased modeling audio retrieval approaches, BoA is a highlevel model due to its perceptual and semantical property. Within the BoA model, a coherency vocabulary indexing structure is adopted to achieve more efficient …


Hybrid Time-Frequency Domain Analysis For Inverter-Fed Induction Motor Fault Detection, T. W. Chua, W. W. Tan, Zhaoxia Wang, C. S. Chang Jul 2010

Hybrid Time-Frequency Domain Analysis For Inverter-Fed Induction Motor Fault Detection, T. W. Chua, W. W. Tan, Zhaoxia Wang, C. S. Chang

Research Collection School Of Computing and Information Systems

The detection of faults in an induction motor is important as a part of preventive maintenance. Stator current is one of the most popular signals used for utility-supplied induction motor fault detection as a current sensor can be installed nonintrusively. In variable speeds operation, the use of an inverter to drive the induction motor introduces noise into the stator current so stator current based fault detection techniques become less reliable. This paper presents a hybrid algorithm, which combines time and frequency domain analysis, for broken rotor bar and bearing fault detection. Cluster information obtained by using Independent Component Analysis (ICA) …


Mental Development And Representation Building Through Motivated Learning, Janusz Starzyk, Pawel Raif, Ah-Hwee Tan Jul 2010

Mental Development And Representation Building Through Motivated Learning, Janusz Starzyk, Pawel Raif, Ah-Hwee Tan

Research Collection School Of Computing and Information Systems

Motivated learning is a new machine learning approach that extends reinforcement learning idea to dynamically changing, and highly structured environments. In this approach a machine is capable of defining its own objectives and learns to satisfy them though an internal reward system. The machine is forced to explore the environment in response to externally applied negative (pain) signals that it must minimize. In doing so, it discovers relationships between objects observed through its sensory inputs and actions it performs on the observed objects. Observed concepts are not predefined but are emerging as a result of successful operations. For the optimum …


Towards Probabilistic Memetic Algorithm: An Initial Study On Capacitated Arc Routing Problem, Liang Feng, Yew-Soon Ong, Quang Huy Nguyen, Ah-Hwee Tan Jul 2010

Towards Probabilistic Memetic Algorithm: An Initial Study On Capacitated Arc Routing Problem, Liang Feng, Yew-Soon Ong, Quang Huy Nguyen, Ah-Hwee Tan

Research Collection School Of Computing and Information Systems

Capacitated arc routing problem (CARP) has attracted much attention due to its generality to many real world problems. Memetic algorithm (MA), among other metaheuristic search methods, has been shown to achieve competitive performances in solving CARP ranging from small to medium size. In this paper we propose a formal probabilistic memetic algorithm for CARP that is equipped with an adaptation mechanism to control the degree of global exploration against local exploitation while the search progresses. Experimental study on benchmark instances of CARP showed that the proposed probabilistic scheme led to improved search performances when introduced into a recently proposed state-of-the-art …


Auditing The Defense Against Cross Site Scripting In Web Applications, Lwin Khin Shar, Hee Beng Kuan Tan Jul 2010

Auditing The Defense Against Cross Site Scripting In Web Applications, Lwin Khin Shar, Hee Beng Kuan Tan

Research Collection School Of Computing and Information Systems

Majority attacks to web applications today are mainly carried out through input manipulation in order to cause unintended actions of these applications. These attacks exploit the weaknesses of web applications in preventing the manipulation of inputs. Among these attacks, cross site scripting attack -- malicious input is submitted to perform unintended actions on a HTML response page -- is a common type of attacks. This paper proposes an approach for thorough auditing of code to defend against cross site scripting attack. Based on the possible methods of implementing defenses against cross site scripting attack, the approach extracts all such defenses …


Impact Of Flow And Brand Equity In 3d Virtual Worlds, Fiona Fui-Hoon Nah, Brenda Eschenbrenner, David Dewester, So Ra Park Jul 2010

Impact Of Flow And Brand Equity In 3d Virtual Worlds, Fiona Fui-Hoon Nah, Brenda Eschenbrenner, David Dewester, So Ra Park

Research Collection School Of Computing and Information Systems

This research is a partial test of Park et al.’s (2008) model to assess the impact of flow and brand equity in 3D virtual worlds. It draws on flow theory as its main theoretical foundation to understand and empirically assess the impact of flow on brand equity and behavioral intention in 3D virtual worlds. The findings suggest that the balance of skills and challenges in 3D virtual worlds influences users’ flow experience, which in turn influences brand equity. Brand equity then increases behavioral intention. The authors also found that the impact of flow on behavioral intention in 3D virtual worlds …


Effective Music Tagging Through Advanced Statistical Modeling, Jialie Shen, Meng Wang, Shuicheng Yan, Hwee Hwa Pang, Xian-Sheng Hua Jul 2010

Effective Music Tagging Through Advanced Statistical Modeling, Jialie Shen, Meng Wang, Shuicheng Yan, Hwee Hwa Pang, Xian-Sheng Hua

Research Collection School Of Computing and Information Systems

Music information retrieval (MIR) holds great promise as a technology for managing large music archives. One of the key components of MIR that has been actively researched into is music tagging. While significant progress has been achieved, most of the existing systems still adopt a simple classification approach, and apply machine learning classifiers directly on low level acoustic features. Consequently, they suffer the shortcomings of (1) poor accuracy, (2) lack of comprehensive evaluation results and the associated analysis based on large scale datasets, and (3) incomplete content representation, arising from the lack of multimodal and temporal information integration. In this …


Generating Templates Of Entity Summaries With An Entity-Aspect Model And Pattern Mining, Peng Li, Jing Jiang, Yinglin Wang Jul 2010

Generating Templates Of Entity Summaries With An Entity-Aspect Model And Pattern Mining, Peng Li, Jing Jiang, Yinglin Wang

Research Collection School Of Computing and Information Systems

In this paper, we propose a novel approach to automatic generation of summary templates from given collections of summary articles. This kind of summary templates can be useful in various applications. We first develop an entity-aspect LDA model to simultaneously cluster both sentences and words into aspects. We then apply frequent subtree pattern mining on the dependency parse trees of the clustered and labeled sentences to discover sentence patterns that well represent the aspects. Key features of our method include automatic grouping of semantically related sentence patterns and automatic identification of template slots that need to be filled in. We …


Evaluation Of Protein Backbone Alphabets: Using Predicted Local Structure For Fold Recognition, Kyong Jin Shim Jul 2010

Evaluation Of Protein Backbone Alphabets: Using Predicted Local Structure For Fold Recognition, Kyong Jin Shim

Research Collection School Of Computing and Information Systems

Optimally combining available information is one of the key challenges in knowledge-driven prediction techniques. In this study, we evaluate six Phi and Psi-based backbone alphabets. We show that the addition of predicted backbone conformations to SVM classifiers can improve fold recognition. Our experimental results show that the inclusion of predicted backbone conformations in our feature representation leads to higher overall accuracy compared to when using amino acid residues alone.


Self-Organizing Agents For Reinforcement Learning In Virtual Worlds, Yilin Kang, Ah-Hwee Tan Jul 2010

Self-Organizing Agents For Reinforcement Learning In Virtual Worlds, Yilin Kang, Ah-Hwee Tan

Research Collection School Of Computing and Information Systems

We present a self-organizing neural model for creating intelligent learning agents in virtual worlds. As agents in a virtual world roam, interact and socialize with users and other agents as in real world without explicit goals and teachers, learning in virtual world presents many challenges not found in typical machine learning benchmarks. In this paper, we highlight the unique issues and challenges of building learning agents in virtual world using reinforcement learning. Specifically, a self-organizing neural model, named TD-FALCON (Temporal Difference - Fusion Architecture for Learning and Cognition), is deployed, which enables an autonomous agent to adapt and function in …


New Constructions For Identity-Based Unidirectional Proxy Re-Encryption, Junzuo Lai, Wen Tao Zhu, Robert H. Deng, Shengli Liu, Weidong Kou Jul 2010

New Constructions For Identity-Based Unidirectional Proxy Re-Encryption, Junzuo Lai, Wen Tao Zhu, Robert H. Deng, Shengli Liu, Weidong Kou

Research Collection School Of Computing and Information Systems

We address the cryptographic topic of proxy re-encryption (PRE), which is a special public-key cryptosystem. A PRE scheme allows a special entity, known as the proxy, to transform a message encrypted with the public key of a delegator (say Alice), into a new ciphertext that is protected under the public key of a delegatee (say Bob), and thus the same message can then be recovered with Bob’s private key. In this paper, in the identity-based setting, we first investigate the relationship between so called mediated encryption and unidirectional PRE. We provide a general framework which converts any secure identity-based unidirectional …


Learning To Rank Only Using Training Data From Related Domain, Wei Gao, Peng Cai, Kam-Fai Wong, Aoying Zhou Jul 2010

Learning To Rank Only Using Training Data From Related Domain, Wei Gao, Peng Cai, Kam-Fai Wong, Aoying Zhou

Research Collection School Of Computing and Information Systems

Like traditional supervised and semi-supervised algorithms, learning to rank for information retrieval requires document annotations provided by domain experts. It is costly to annotate training data for different search domains and tasks. We propose to exploit training data annotated for a related domain to learn to rank retrieved documents in the target domain, in which no labeled data is available. We present a simple yet effective approach based on instance-weighting scheme. Our method first estimates the importance of each related-domain document relative to the target domain. Then heuristics are studied to transform the importance of individual documents to the pairwise …


Effective Heuristic Methods For Finding Non-Optimal Solutions Of Interest In Constrained Optimization Models, Steven O. Kimbrough, Ann Kuo, Hoong Chuin Lau Jul 2010

Effective Heuristic Methods For Finding Non-Optimal Solutions Of Interest In Constrained Optimization Models, Steven O. Kimbrough, Ann Kuo, Hoong Chuin Lau

Research Collection School Of Computing and Information Systems

This paper introduces the SoI problem, that of finding nonoptimal solutions of interest for constrained optimization models. SoI problems subsume finding FoIs (feasible solutions of interest), and IoIs (infeasible solutions of interest). In all cases, the interest addressed is post-solution analysis in one form or another. Post-solution analysis of a constrained optimization model occurs after the model has been solved and a good or optimal solution for it has been found. At this point, sensitivity analysis and other questions of import for decision making (discussed in the paper) come into play and for this purpose the SoIs can be of …


A Self-Organizing Approach To Episodic Memory Modeling, Wenwen Wang, Budhitama Subagdja, Ah-Hwee Tan Jul 2010

A Self-Organizing Approach To Episodic Memory Modeling, Wenwen Wang, Budhitama Subagdja, Ah-Hwee Tan

Research Collection School Of Computing and Information Systems

This paper presents a neural model that learns episodic traces in response to a continual stream of sensory input and feedback received from the environment. The proposed model, based on fusion Adaptive Resonance Theory (fusion ART) network, extracts key events and encodes spatiotemporal relations between events by creating cognitive nodes dynamically. The model further incorporates a novel memory search procedure, which performs parallel search of stored episodic traces continuously. Comparing with prior systems, the proposed episodic memory model presents a robust approach to encoding key events and episodes and recalling them using partial and erroneous cues. We present experimental studies, …


On The Sampling Of Web Images For Learning Visual Concept Classifiers, Shiai Zhu, Gang Wang, Chong-Wah Ngo, Yu-Gang Jiang Jul 2010

On The Sampling Of Web Images For Learning Visual Concept Classifiers, Shiai Zhu, Gang Wang, Chong-Wah Ngo, Yu-Gang Jiang

Research Collection School Of Computing and Information Systems

Visual concept learning often requires a large set of training images. In practice, nevertheless, acquiring noise-free training labels with sufficient positive examples is always expensive. A plausible solution for training data collection is by sampling the largely available user-tagged images from social media websites. With the general belief that the probability of correct tagging is higher than that of incorrect tagging, such a solution often sounds feasible, though is not without challenges. First, user-tags can be subjective and, to certain extent, are ambiguous. For instance, an image tagged with “whales” may be simply a picture about ocean museum. Learning concept …


Self-Organizing Neural Networks For Behavior Modeling In Games, Shu Feng, Ah-Hwee Tan Jul 2010

Self-Organizing Neural Networks For Behavior Modeling In Games, Shu Feng, Ah-Hwee Tan

Research Collection School Of Computing and Information Systems

This paper proposes self-organizing neural networks for modeling behavior of non-player characters (NPC) in first person shooting games. Specifically, two classes of self-organizing neural models, namely Self-Generating Neural Networks (SGNN) and Fusion Architecture for Learning and Cognition (FALCON) are used to learn non-player characters' behavior rules according to recorded patterns. Behavior learning abilities of these two models are investigated by learning specific sample Bots in the Unreal Tournament game in a supervised manner. Our empirical experiments demonstrate that both SGNN and FALCON are able to recognize important behavior patterns and learn the necessary knowledge to operate in the Unreal environment. …


Faceted Topic Retrieval Of News Video Using Joint Topic Modeling Of Visual Features And Speech Transcripts, Kong-Wah Wan, Ah-Hwee Tan, Joo-Hwee Lim, Liang-Tien Chia Jul 2010

Faceted Topic Retrieval Of News Video Using Joint Topic Modeling Of Visual Features And Speech Transcripts, Kong-Wah Wan, Ah-Hwee Tan, Joo-Hwee Lim, Liang-Tien Chia

Research Collection School Of Computing and Information Systems

Because of the inherent ambiguity in user queries, an important task of modern retrieval systems is faceted topic retrieval (FTR), which relates to the goal of returning diverse or novel information elucidating the wide range of topics or facets of the query need. We introduce a generative model for hypothesizing facets in the (news) video domain by combining the complementary information in the visual keyframes and the speech transcripts. We evaluate the efficacy of our multimodal model on the standard TRECVID-2005 video corpus annotated with facets. We find that: (1) the joint modeling of the visual and text (speech transcripts) …


Show Me The Numbers: Visual Analytics For Insights, Tin Seong Kam Jul 2010

Show Me The Numbers: Visual Analytics For Insights, Tin Seong Kam

Research Collection School Of Computing and Information Systems

In this highly volatile and fast-paced financial market, traders and managers working in banking and financial organizations must struggle to cope with large and complex data from multi-sources, that move throughout the market at increasingly high speed. The cost of making poor business and investment decisions is very high. This places great demands on data analysts, who are responsible for providing process information, to support the activities of traders and managers. Static reports and traditional business intelligence tools simply cannot keep up with a market that is changing on a second-to-second basis. By the time the traders and bankers have …


A Heuristic Algorithm For Trust-Oriented Service Provider Selection In Complex Social Networks, Guanfeng Liu, Yan Wang, Mehmet A. Orgun, Ee Peng Lim Jul 2010

A Heuristic Algorithm For Trust-Oriented Service Provider Selection In Complex Social Networks, Guanfeng Liu, Yan Wang, Mehmet A. Orgun, Ee Peng Lim

Research Collection School Of Computing and Information Systems

In a service-oriented online social network consisting of service providers and consumers, a service consumer can search trustworthy service providers via the social network. This requires the evaluation of the trustworthiness of a service provider along a certain social trust path from the service consumer to the service provider. However, there are usually many social trust paths between participants in social networks. Thus, a challenging problem is which social trust path is the optimal one that can yield the most trustworthy evaluation result. In this paper, we first present a novel complex social network structure and a new concept, Quality …


Extracting Common Emotions From Blogs Based On Fine-Grained Sentiment Clustering, Shi Feng, Daling Wang, Ge Yu, Wei Gao, Kam-Fai Wong Jul 2010

Extracting Common Emotions From Blogs Based On Fine-Grained Sentiment Clustering, Shi Feng, Daling Wang, Ge Yu, Wei Gao, Kam-Fai Wong

Research Collection School Of Computing and Information Systems

Recently, blogs have emerged as the major platform for people to express their feelings and sentiments in the age of Web 2.0. The common emotions, which reflect people’s collective and overall sentiments, are becoming the major concern for governments, business companies and individual users. Different from previous literatures on sentiment classification and summarization, the major issue of common emotion extraction is to find out people’s collective sentiments and their corresponding distributions on the Web. Most existing blog clustering methods take into account keywords, stories or timelines but neglect the embedded sentiments, which are considered very important features of blogs. In …


Analytics-Modulated Coding Of Surveillance Video, Lai-Tee Cheok, Nikhil Gagvani Jul 2010

Analytics-Modulated Coding Of Surveillance Video, Lai-Tee Cheok, Nikhil Gagvani

Research Collection School Of Computing and Information Systems

Video surveillance systems increasingly use H.264 coding to achieve 24x7 recording and streaming. However, with the proliferation of security cameras, and the need to store several months of video, bandwidth and storage costs can be significant. We propose a new compression technique to significantly improve the coding efficiency of H.264 for surveillance video. Video content is analyzed and video semantics are extracted using video analytics algorithms such as segmentation, classification and tracking. In contrast to existing approaches, our Analytics-Modulated Compression (AMC) scheme does not require coding of object shape information and produces bitstreams that are standards-compliant and not limited to …


Semantics-Preserving Bag-Of-Words Models And Applications, Lei Wu, Steven C. H. Hoi, Nenghai Yu Jul 2010

Semantics-Preserving Bag-Of-Words Models And Applications, Lei Wu, Steven C. H. Hoi, Nenghai Yu

Research Collection School Of Computing and Information Systems

The Bag-of-Words (BoW) model is a promising image representation technique for image categorization and annotation tasks. One critical limitation of existing BoW models is that much semantic information is lost during the codebook generation process, an important step of BoW. This is because the codebook generated by BoW is often obtained via building the codebook simply by clustering visual features in Euclidian space. However, visual features related to the same semantics may not distribute in clusters in the Euclidian space, which is primarily due to the semantic gap between low-level features and high-level semantics. In this paper, we propose a …