Browsing by Subject "Multiplication-free operator"

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    L1 norm based multiplication-free cosine similarity measures for big data analysis
    (IEEE, 2014-11) Akbaş, Cem Emre; Bozkurt, Alican; Arslan, Musa Tunç; Aslanoğlu, Hüseyin; Çetin, A. Enis
    The cosine similarity measure is widely used in big data analysis to compare vectors. In this article a new set of vector similarity measures are proposed. New vector similarity measures are based on a multiplication-free operator which requires only additions and sign operations. A vector 'product' using the multiplication-free operator is also defined. The new vector product induces the ℓ1-norm. As a result, new cosine measure-like similarity measures are normalized by the ℓ1-norms of the vectors. They can be computed using the MapReduce framework. Simulation examples are presented. © 2014 IEEE.
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    Non-euclidean vector product for neural networks
    (IEEE, 2018-04) Afrasiyabi, A.; Badawi, Diaa; Nasır, B.; Yıldız, O.; Yarman- Vural, F. T.; Çetin, A. Enis
    We present a non-Euclidean vector product for artificial neural networks. The vector product operator does not require any multiplications while providing correlation information between two vectors. Ordinary neurons require inner product of two vectors. We propose a class of neural networks with the universal approximation property over the space of Lebesgue integrable functions based on the proposed non-Euclidean vector product. In this new network, the 'product' of two real numbers is defined as the sum of their absolute values, with the sign determined by the sign of the product of the numbers. This 'product' is used to construct a vector product in RN. The vector product induces the l1 norm. The additive neural network successfully solves the XOR problem. Experiments on MNIST and CIFAR datasets show that the classification performance of the proposed additive neural network is comparable to the corresponding multi-layer perceptron and convolutional neural networks.