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Norm Adjusted Proximity Graph for Fast Inner Product Retrieval
Knowledge Discovery and Data Mining, 2021Efficient inner product search on embedding vectors is often the vital stage for online ranking services, such as recommendation and information retrieval.
Shulong Tan +5 more
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Simple Yet Efficient Algorithms for Maximum Inner Product Search via Extreme Order Statistics
Knowledge Discovery and Data Mining, 2021We present a novel dimensionality reduction method for the approximate maximum inner product search (MIPS), named CEOs, based on the theory of concomitants of extreme order statistics. Utilizing the asymptotic behavior of these concomitants, we show that
Ninh D. Pham
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Comments on “Fuzzy inner product spaces”
Fuzzy Sets and Systems, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jian-Zhong Xiao, Feng-Qin Zhu
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Privacy-Preserving WiFi Localization Based on Inner Product Encryption in a Cloud Environment
IEEE Internet of Things JournalCloud-based indoor positioning services have advantages over noncloud methods but also confront serious privacy concerns. Existing privacy-preserving schemes are designed for conventional two-entity localization models thus not applicable to the cloud ...
Zhiheng Wang +4 more
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Inner product inequalities with applications
Linear and multilinear algebraIn this paper, we show some inner product inequalities, which can be considered of Cauchy-Schwarz and Buzano type inequalities for Hilbert space operators. This will lead to several applications that include a new equivalent statement to the fact that an
M. Sababheh, H. Moradi, Satyajit Sahoo
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On a Characterisation of Inner Product Spaces
gmj, 2001Abstract It is well known that for the Hilbert space H the minimum value of the functional F μ (f) = ∫ H ‖f – g‖2 dμ(g), f ∈ H, is achived at the mean of μ for any probability measure μ with strong second moment on H.
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Correction to: “Inner Product Spaces”
The American Mathematical Monthly, 1975(1975). Correction to: “Inner Product Spaces”. The American Mathematical Monthly: Vol. 82, No. 3, pp. 251-252.
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On tuples of commuting operators in positive semidefinite inner product spaces
, 2020This paper is concerned with the study of certain properties of operator tuples on a complex Hilbert space H when a semi-inner product induced by a positive operator A on H is considered.
Kais Feki
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1978
So far in our study of vector spaces and linear transformations we have made no use of the notions of length and angle, although these concepts play an important role in our intuition for the vector algebra of ℝ2 and ℝ3. In fact the length of a vector and the angle between two vectors play very important parts in the further development of linear ...
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So far in our study of vector spaces and linear transformations we have made no use of the notions of length and angle, although these concepts play an important role in our intuition for the vector algebra of ℝ2 and ℝ3. In fact the length of a vector and the angle between two vectors play very important parts in the further development of linear ...
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2018
In Chap. 1 we defined a vector space as an abstraction of the familiar Euclidean space. In doing so, we took into account only two aspects of the set of vectors in a plane, namely the vector addition and scalar multiplication. Now, we consider the third aspect, namely the angle between vectors.
M. Thamban Nair, Arindama Singh
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In Chap. 1 we defined a vector space as an abstraction of the familiar Euclidean space. In doing so, we took into account only two aspects of the set of vectors in a plane, namely the vector addition and scalar multiplication. Now, we consider the third aspect, namely the angle between vectors.
M. Thamban Nair, Arindama Singh
openaire +2 more sources