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Related Concept Videos

Scalar and Vector Triple Products01:06

Scalar and Vector Triple Products

Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
The scalar triple product is the dot product of a vector with the cross product of two vectors.
Scalar Product (Dot Product)01:11

Scalar Product (Dot Product)

The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a number, that is, a scalar quantity. Scalar products are used to define work and energy relations. For example, the work that a force (a vector) performs on an object while causing its displacement (a vector) is defined as a scalar product of the force vector with the displacement vector.
The scalar product of two vectors is obtained by multiplying...

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Related Experiment Video

Updated: Jul 12, 2026

Quantitation of Protein Expression and Co-localization Using Multiplexed Immuno-histochemical Staining and Multispectral Imaging
08:40

Quantitation of Protein Expression and Co-localization Using Multiplexed Immuno-histochemical Staining and Multispectral Imaging

Published on: April 8, 2016

The Scalable Tensor-based Codebook Product Quantization for Multi-Label Image Retrieval.

Bin Luo, Laurence T Yang, Debin Liu

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |July 9, 2026
    PubMed
    Summary
    This summary is machine-generated.

    Tensor-based Codebook Product Quantization (TCPQ) addresses limitations in scalable product quantization for image retrieval. TCPQ captures correlations and uses lightweight codebooks, achieving state-of-the-art performance.

    Related Experiment Videos

    Last Updated: Jul 12, 2026

    Quantitation of Protein Expression and Co-localization Using Multiplexed Immuno-histochemical Staining and Multispectral Imaging
    08:40

    Quantitation of Protein Expression and Co-localization Using Multiplexed Immuno-histochemical Staining and Multispectral Imaging

    Published on: April 8, 2016

    Area of Science:

    • Computer Science
    • Artificial Intelligence
    • Machine Learning

    Background:

    • Scalable product quantization is crucial for large-scale image retrieval.
    • Existing methods often ignore correlations within sub-codebooks and codewords.
    • Memory consumption increases significantly with more subspaces or codewords.

    Purpose of the Study:

    • To propose a novel scalable product quantization framework, Tensor-based Codebook Product Quantization (TCPQ).
    • To address limitations in approximating similarity, capturing correlations, and managing memory consumption.
    • To integrate tensor theory with product quantization for enhanced image retrieval.

    Main Methods:

    • Developed a Tensor-based Codebook Product Quantization (TCPQ) framework within an end-to-end network.
    • Utilized tensor-based methods to capture spatial correlations among sub-codebooks and codewords.
    • Employed lightweight codebooks for efficiency and a subspace-wise unbiased supervised contrastive loss for optimization.
    • Incorporated ArcFace loss and an orthogonality constraint to improve feature discriminability and prevent overfitting.

    Main Results:

    • TCPQ effectively captures spatial correlations among sub-codebooks and codewords.
    • The proposed loss function enhances class separability and regulates sample distances within quantization subspaces.
    • ArcFace loss and orthogonality constraints boosted feature discriminative power and model stability.
    • Achieved state-of-the-art retrieval performance on three large-scale benchmarks.

    Conclusions:

    • TCPQ offers an innovative approach to scalable product quantization by integrating tensor theory.
    • The framework demonstrates superior performance in large-scale image retrieval tasks.
    • TCPQ provides an efficient and effective solution for handling correlations and memory constraints in quantization.