Quadratic Form

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Thomas Seidl - One of the best experts on this subject based on the ideXlab platform.

  • earth mover s distance vs Quadratic Form distance an analytical and empirical comparison
    International Symposium on Multimedia, 2015
    Co-Authors: Christian Beecks, Merih Seran Uysal, Thomas Seidl
    Abstract:

    It has been past more than a decade since the Earth Mover's Distance and the Quadratic Form Distance have been proposed as distance-based similarity measures for color-based image similarity. Ever since their utilization in various domains, they have developed into major general-purpose distance functions. In this paper, we subject both dissimilarity measures to a fundamental analytical and empirical analysis in order to reveal their strengths and weaknesses.

  • modeling image similarity by gaussian mixture models and the signature Quadratic Form distance
    International Conference on Computer Vision, 2011
    Co-Authors: Christian Beecks, Anca Maria Ivanescu, Steffen Kirchhoff, Thomas Seidl
    Abstract:

    Modeling image similarity for browsing and searching in voluminous image databases is a challenging task of nearly all content-based image retrieval systems. One promising way of defining image similarity consists in applying distance-based similarity measures on compact image representations. Beyond feature histograms and feature signatures, more general feature representations are mixture models of which the Gaussian mixture model is the most prominent one. This feature representation can be compared by employing approximations of the Kullback-Leibler Divergence. Although several of those approximations have been successfully applied to model image similarity, their applicability to mixture models based on high-dimensional feature descriptors is questionable. In this paper, we thus introduce the Signature Quadratic Form Distance to measure the distance between two Gaussian mixture models of high-dimensional feature descriptors. We show the analytical computation of the proposed Gaussian Quadratic Form Distance and evaluate its retrieval perFormance by making use of different benchmark image databases.

  • processing the signature Quadratic Form distance on many core gpu architectures
    Conference on Information and Knowledge Management, 2011
    Co-Authors: Martin Krulis, Christian Beecks, Jakub Lokoc, Tomas Skopal, Thomas Seidl
    Abstract:

    The Signature Quadratic Form Distance on feature signatures represents a flexible distance-based similarity model for effective content-based multimedia retrieval. Although metric indexing approaches are able to speed up query processing by two orders of magnitude, their applicability to large-scale multimedia databases containing billions of images is still a challenging issue. In this paper, we propose the utilization of GPUs for efficient query processing with the Signature Quadratic Form Distance. We show how to process multiple distance computations in parallel and demonstrate efficient query processing by comparing many-core GPU with multi-core CPU implementations.

  • indexing the signature Quadratic Form distance for efficient content based multimedia retrieval
    International Conference on Multimedia Retrieval, 2011
    Co-Authors: Christian Beecks, Thomas Seidl, Jakub Lokoc, Tomas Skopal
    Abstract:

    The Signature Quadratic Form Distance has been introduced as an adaptive similarity measure coping with flexible content representations of various multimedia data. Although the Signature Quadratic Form Distance has shown good retrieval perFormance with respect to their qualities of effectiveness and efficiency, its applicability to index structures remains a challenging issue due to its dynamic nature. In this paper, we investigate the indexability of the Signature Quadratic Form Distance regarding metric access methods. We show how the distance's inherent parameters determine the indexability and analyze the relationship between effectiveness and efficiency on numerous image databases.

  • ICCV - Modeling image similarity by Gaussian mixture models and the Signature Quadratic Form Distance
    2011 International Conference on Computer Vision, 2011
    Co-Authors: Christian Beecks, Anca Maria Ivanescu, Steffen Kirchhoff, Thomas Seidl
    Abstract:

    Modeling image similarity for browsing and searching in voluminous image databases is a challenging task of nearly all content-based image retrieval systems. One promising way of defining image similarity consists in applying distance-based similarity measures on compact image representations. Beyond feature histograms and feature signatures, more general feature representations are mixture models of which the Gaussian mixture model is the most prominent one. This feature representation can be compared by employing approximations of the Kullback-Leibler Divergence. Although several of those approximations have been successfully applied to model image similarity, their applicability to mixture models based on high-dimensional feature descriptors is questionable. In this paper, we thus introduce the Signature Quadratic Form Distance to measure the distance between two Gaussian mixture models of high-dimensional feature descriptors. We show the analytical computation of the proposed Gaussian Quadratic Form Distance and evaluate its retrieval perFormance by making use of different benchmark image databases.

A P Liavas - One of the best experts on this subject based on the ideXlab platform.

  • efficient computation of the binary vector that maximizes a rank deficient Quadratic Form
    IEEE Transactions on Information Theory, 2010
    Co-Authors: George N Karystinos, A P Liavas
    Abstract:

    The maximization of a full-rank Quadratic Form over the binary alphabet can be perFormed through exponential-complexity exhaustive search. However, if the rank of the Form is not a function of the problem size, then it can be maximized in polynomial time. By introducing auxiliary spherical coordinates, we show that the rank-deficient Quadratic-Form maximization problem is converted into a double maximization of a linear Form over a multidimensional continuous set, the multidimensional set is partitioned into a polynomial-size set of regions which are associated with distinct candidate binary vectors, and the optimal binary vector belongs to the polynomial-size set of candidate vectors. Thus, the size of the candidate set is reduced from exponential to polynomial. We also develop an algorithm that constructs the polynomial-size candidate set in polynomial time and show that it is fully parallelizable and rank-scalable. Finally, we demonstrate the efficiency of the proposed algorithm in the context of adaptive spreading code design.

  • ISIT - Quadratic Form maximization over the binary field with polynomial complexity
    2008 IEEE International Symposium on Information Theory, 2008
    Co-Authors: George N Karystinos, A P Liavas
    Abstract:

    We consider the maximization of a Quadratic Form over the binary alphabet. By introducing auxiliary spherical coordinates, we show that if the rank of the Form is not a function of the problem size, then (i) the multidimensional space is partitioned into a polynomial-size set of regions which are associated with distinct binary vectors and (ii) the binary vector that maximizes the rank-deficient Quadratic Form belongs to the polynomial-size set of candidate vectors. Thus, the size of the feasible set of candidate vectors is efficiently reduced from exponential to polynomial. We also develop an algorithm that constructs the polynomial-size feasible set in polynomial time and show that it is fully parallelizable and rank-scalable. Finally, we examine the efficiency of the proposed algorithm in the context of multiple-input multiple-output signal detection.

  • efficient computation of the binary vector that maximizes a rank deficient Quadratic Form
    International Conference on Acoustics Speech and Signal Processing, 2008
    Co-Authors: George N Karystinos, A P Liavas
    Abstract:

    The maximization of a full-rank Quadratic Form over a finite alphabet is NP-hard in both a worst-case sense and an average sense. Interestingly, if the rank of the Form is not a function of the problem size, then it can be maximized in polynomial time. An algorithm for the efficient computation of the binary vector that maximizes a rank-deficient Quadratic Form is developed based on an analytic procedure. Auxiliary spherical coordinates are introduced and the multi-dimensional space is partitioned into a polynomial-size set of regions; each region corresponds to a distinct binary vector. The binary vector that maximizes the rank-deficient Quadratic Form is shown to belong to the polynomial-size set of candidate vectors. Thus, the size of the feasible set is efficiently reduced from exponential to polynomial.

  • ICASSP - Efficient computation of the binary vector that maximizes a rank-deficient Quadratic Form
    2008 IEEE International Conference on Acoustics Speech and Signal Processing, 2008
    Co-Authors: George N Karystinos, A P Liavas
    Abstract:

    The maximization of a full-rank Quadratic Form over a finite alphabet is NP-hard in both a worst-case sense and an average sense. Interestingly, if the rank of the Form is not a function of the problem size, then it can be maximized in polynomial time. An algorithm for the efficient computation of the binary vector that maximizes a rank-deficient Quadratic Form is developed based on an analytic procedure. Auxiliary spherical coordinates are introduced and the multi-dimensional space is partitioned into a polynomial-size set of regions; each region corresponds to a distinct binary vector. The binary vector that maximizes the rank-deficient Quadratic Form is shown to belong to the polynomial-size set of candidate vectors. Thus, the size of the feasible set is efficiently reduced from exponential to polynomial.

George N Karystinos - One of the best experts on this subject based on the ideXlab platform.

  • rank deficient Quadratic Form maximization over m phase alphabet polynomial complexity solvability and algorithmic developments
    International Conference on Acoustics Speech and Signal Processing, 2011
    Co-Authors: Anastasios Kyrillidis, George N Karystinos
    Abstract:

    The maximization of a positive (semi)definite complex Quadratic Form over a finite alphabet is NP-hard and achieved through exhaustive search when the Form has full rank. However, if the Form is rank-deficient, the optimal solution can be computed with only polynomial complexity in the length N of the maximizing vector. In this work, we consider the general case of a rank-D positive (semi)definite complex Quadratic Form and develop a method that maximizes the Form with respect to a M-phase vector with polynomial complexity. The proposed method efficiently reduces the size of the feasible set from exponential to polynomial. We also develop an algorithm that constructs the polynomial-size candidate set in polynomial time and observe that it is fully parallelizable and rank-scalable.

  • efficient computation of the binary vector that maximizes a rank deficient Quadratic Form
    IEEE Transactions on Information Theory, 2010
    Co-Authors: George N Karystinos, A P Liavas
    Abstract:

    The maximization of a full-rank Quadratic Form over the binary alphabet can be perFormed through exponential-complexity exhaustive search. However, if the rank of the Form is not a function of the problem size, then it can be maximized in polynomial time. By introducing auxiliary spherical coordinates, we show that the rank-deficient Quadratic-Form maximization problem is converted into a double maximization of a linear Form over a multidimensional continuous set, the multidimensional set is partitioned into a polynomial-size set of regions which are associated with distinct candidate binary vectors, and the optimal binary vector belongs to the polynomial-size set of candidate vectors. Thus, the size of the candidate set is reduced from exponential to polynomial. We also develop an algorithm that constructs the polynomial-size candidate set in polynomial time and show that it is fully parallelizable and rank-scalable. Finally, we demonstrate the efficiency of the proposed algorithm in the context of adaptive spreading code design.

  • ISIT - Quadratic Form maximization over the binary field with polynomial complexity
    2008 IEEE International Symposium on Information Theory, 2008
    Co-Authors: George N Karystinos, A P Liavas
    Abstract:

    We consider the maximization of a Quadratic Form over the binary alphabet. By introducing auxiliary spherical coordinates, we show that if the rank of the Form is not a function of the problem size, then (i) the multidimensional space is partitioned into a polynomial-size set of regions which are associated with distinct binary vectors and (ii) the binary vector that maximizes the rank-deficient Quadratic Form belongs to the polynomial-size set of candidate vectors. Thus, the size of the feasible set of candidate vectors is efficiently reduced from exponential to polynomial. We also develop an algorithm that constructs the polynomial-size feasible set in polynomial time and show that it is fully parallelizable and rank-scalable. Finally, we examine the efficiency of the proposed algorithm in the context of multiple-input multiple-output signal detection.

  • efficient computation of the binary vector that maximizes a rank deficient Quadratic Form
    International Conference on Acoustics Speech and Signal Processing, 2008
    Co-Authors: George N Karystinos, A P Liavas
    Abstract:

    The maximization of a full-rank Quadratic Form over a finite alphabet is NP-hard in both a worst-case sense and an average sense. Interestingly, if the rank of the Form is not a function of the problem size, then it can be maximized in polynomial time. An algorithm for the efficient computation of the binary vector that maximizes a rank-deficient Quadratic Form is developed based on an analytic procedure. Auxiliary spherical coordinates are introduced and the multi-dimensional space is partitioned into a polynomial-size set of regions; each region corresponds to a distinct binary vector. The binary vector that maximizes the rank-deficient Quadratic Form is shown to belong to the polynomial-size set of candidate vectors. Thus, the size of the feasible set is efficiently reduced from exponential to polynomial.

  • ICASSP - Efficient computation of the binary vector that maximizes a rank-deficient Quadratic Form
    2008 IEEE International Conference on Acoustics Speech and Signal Processing, 2008
    Co-Authors: George N Karystinos, A P Liavas
    Abstract:

    The maximization of a full-rank Quadratic Form over a finite alphabet is NP-hard in both a worst-case sense and an average sense. Interestingly, if the rank of the Form is not a function of the problem size, then it can be maximized in polynomial time. An algorithm for the efficient computation of the binary vector that maximizes a rank-deficient Quadratic Form is developed based on an analytic procedure. Auxiliary spherical coordinates are introduced and the multi-dimensional space is partitioned into a polynomial-size set of regions; each region corresponds to a distinct binary vector. The binary vector that maximizes the rank-deficient Quadratic Form is shown to belong to the polynomial-size set of candidate vectors. Thus, the size of the feasible set is efficiently reduced from exponential to polynomial.

Christian Beecks - One of the best experts on this subject based on the ideXlab platform.

  • earth mover s distance vs Quadratic Form distance an analytical and empirical comparison
    International Symposium on Multimedia, 2015
    Co-Authors: Christian Beecks, Merih Seran Uysal, Thomas Seidl
    Abstract:

    It has been past more than a decade since the Earth Mover's Distance and the Quadratic Form Distance have been proposed as distance-based similarity measures for color-based image similarity. Ever since their utilization in various domains, they have developed into major general-purpose distance functions. In this paper, we subject both dissimilarity measures to a fundamental analytical and empirical analysis in order to reveal their strengths and weaknesses.

  • modeling image similarity by gaussian mixture models and the signature Quadratic Form distance
    International Conference on Computer Vision, 2011
    Co-Authors: Christian Beecks, Anca Maria Ivanescu, Steffen Kirchhoff, Thomas Seidl
    Abstract:

    Modeling image similarity for browsing and searching in voluminous image databases is a challenging task of nearly all content-based image retrieval systems. One promising way of defining image similarity consists in applying distance-based similarity measures on compact image representations. Beyond feature histograms and feature signatures, more general feature representations are mixture models of which the Gaussian mixture model is the most prominent one. This feature representation can be compared by employing approximations of the Kullback-Leibler Divergence. Although several of those approximations have been successfully applied to model image similarity, their applicability to mixture models based on high-dimensional feature descriptors is questionable. In this paper, we thus introduce the Signature Quadratic Form Distance to measure the distance between two Gaussian mixture models of high-dimensional feature descriptors. We show the analytical computation of the proposed Gaussian Quadratic Form Distance and evaluate its retrieval perFormance by making use of different benchmark image databases.

  • processing the signature Quadratic Form distance on many core gpu architectures
    Conference on Information and Knowledge Management, 2011
    Co-Authors: Martin Krulis, Christian Beecks, Jakub Lokoc, Tomas Skopal, Thomas Seidl
    Abstract:

    The Signature Quadratic Form Distance on feature signatures represents a flexible distance-based similarity model for effective content-based multimedia retrieval. Although metric indexing approaches are able to speed up query processing by two orders of magnitude, their applicability to large-scale multimedia databases containing billions of images is still a challenging issue. In this paper, we propose the utilization of GPUs for efficient query processing with the Signature Quadratic Form Distance. We show how to process multiple distance computations in parallel and demonstrate efficient query processing by comparing many-core GPU with multi-core CPU implementations.

  • ptolemaic indexing of the signature Quadratic Form distance
    Similarity Search and Applications, 2011
    Co-Authors: Jakub Lokoc, Magnus Lie Hetland, Tomas Skopal, Christian Beecks
    Abstract:

    The signature Quadratic Form distance has been introduced as an adaptive similarity measure coping with flexible content representations of multimedia data. While this distance has shown high retrieval quality, its high computational complexity underscores the need for efficient search methods. Recent research has shown that a huge improvement in search efficiency is achieved when using metric indexing. In this paper, we analyze the applicability of Ptolemaic indexing to the signature Quadratic Form distance. We show that it is a Ptolemaic metric and present an application of Ptolemaic pivot tables to image databases, resolving queries nearly four times as fast as the state-of-the-art metric solution, and up to 300 times as fast as sequential scan.

  • indexing the signature Quadratic Form distance for efficient content based multimedia retrieval
    International Conference on Multimedia Retrieval, 2011
    Co-Authors: Christian Beecks, Thomas Seidl, Jakub Lokoc, Tomas Skopal
    Abstract:

    The Signature Quadratic Form Distance has been introduced as an adaptive similarity measure coping with flexible content representations of various multimedia data. Although the Signature Quadratic Form Distance has shown good retrieval perFormance with respect to their qualities of effectiveness and efficiency, its applicability to index structures remains a challenging issue due to its dynamic nature. In this paper, we investigate the indexability of the Signature Quadratic Form Distance regarding metric access methods. We show how the distance's inherent parameters determine the indexability and analyze the relationship between effectiveness and efficiency on numerous image databases.

Merih Seran Uysal - One of the best experts on this subject based on the ideXlab platform.

  • earth mover s distance vs Quadratic Form distance an analytical and empirical comparison
    International Symposium on Multimedia, 2015
    Co-Authors: Christian Beecks, Merih Seran Uysal, Thomas Seidl
    Abstract:

    It has been past more than a decade since the Earth Mover's Distance and the Quadratic Form Distance have been proposed as distance-based similarity measures for color-based image similarity. Ever since their utilization in various domains, they have developed into major general-purpose distance functions. In this paper, we subject both dissimilarity measures to a fundamental analytical and empirical analysis in order to reveal their strengths and weaknesses.

  • signature Quadratic Form distance
    Conference on Image and Video Retrieval, 2010
    Co-Authors: Christian Beecks, Merih Seran Uysal, Thomas Seidl
    Abstract:

    The Signature Quadratic Form Distance is an adaptive similarity measure for flexible content-based feature representations of multimedia data. In this paper, we present a deep survey of the mathematical foundation of this similarity measure which encompasses the classic Quadratic Form Distance defined only for the comparison between two feature histograms of the same length and structure. Moreover, we give the benefits of the Signature Quadratic Form Distance and experimental evaluation on numerous real-world databases.

  • efficient k nearest neighbor queries with the signature Quadratic Form distance
    International Conference on Data Engineering, 2010
    Co-Authors: Christian Beecks, Merih Seran Uysal, Thomas Seidl
    Abstract:

    A frequently encountered query type in multimedia databases is the k-nearest neighbor query which finds the k-nearest neighbors of a given query. To speed up such queries and to meet the user requirements in low response time, approximation techniques play an important role. In this paper, we present an efficient approximation technique applicable to distance measures defined over flexible feature representations, i.e. feature signatures. We apply our approximation technique to the recently proposed Signature Quadratic Form Distance applicable to feature signatures. We perFormed our experiments on numerous image databases, gathering k-nearest neighbor query rankings in significantly low computation time with an average speed-up factor of 13.

  • SISAP - Similarity matrix compression for efficient signature Quadratic Form distance computation
    Proceedings of the Third International Conference on SImilarity Search and APplications - SISAP '10, 2010
    Co-Authors: Christian Beecks, Merih Seran Uysal, Thomas Seidl
    Abstract:

    Determining similarities among multimedia objects is a fundamental task in many content-based retrieval, analysis, mining, and exploration applications. Among state-of-the-art similarity measures, the Signature Quadratic Form Distance has shown good applicability and high quality in comparing flexible feature representations. In order to improve the efficiency of the Signature Quadratic Form Distance, we propose the similarity matrix compression approach which aims at compressing the distance's inherent similarity matrix. We theoretically show how to reduce the complexity of distance computations and benchmark computation time improvements. As a result, we improve the efficiency of a single distance computation by a factor up to 9.

  • CIVR - Signature Quadratic Form Distance
    Proceedings of the ACM International Conference on Image and Video Retrieval - CIVR '10, 2010
    Co-Authors: Christian Beecks, Merih Seran Uysal, Thomas Seidl
    Abstract:

    The Signature Quadratic Form Distance is an adaptive similarity measure for flexible content-based feature representations of multimedia data. In this paper, we present a deep survey of the mathematical foundation of this similarity measure which encompasses the classic Quadratic Form Distance defined only for the comparison between two feature histograms of the same length and structure. Moreover, we give the benefits of the Signature Quadratic Form Distance and experimental evaluation on numerous real-world databases.