Supervised Categorical Metric Learning With Schatten p-Norms
نویسندگان
چکیده
منابع مشابه
The Quantum Complexity of Computing Schatten $p$-norms
We consider the quantum complexity of computing Schatten p-norms and related quantities, and find that the problem of estimating these quantities is closely related to the one clean qubit model of computation. We show that the problem of approximating Tr(|A|) for a log-local n-qubit Hamiltonian A and p = poly(n), up to a suitable level of accuracy, is contained in DQC1; and that approximating t...
متن کاملSupervised Metric Learning with Generalization Guarantees
In recent years, the crucial importance of metrics in machine learning algorithms has led to anincreasing interest in optimizing distance and similarity functions using knowledge from training data to makethem suitable for the problem at hand. This area of research is known as metric learning. Existing methodstypically aim at optimizing the parameters of a given metric with respect ...
متن کاملHandling Incomplete Categorical Data for Supervised Learning
Classification is an important research topic in knowledge discovery. Most of the researches on classification concern that a complete dataset is given as a training dataset and the test data contain all values of attributes without missing. Unfortunately, incomplete data usually exist in real-world applications. In this paper, we propose new handling schemes of learning classification models f...
متن کاملSchatten norms of Toeplitz matrices with Fisher-Hartwig singularities
The asymptotics of the Schatten norms of finite Toeplitz matrices generated by functions with a Fisher-Hartwig singularity are described as the matrix dimension n goes to infinity. The message of the paper is to reveal some kind of a kink: the pth Schatten norm increases as n to the power 1/p before the singularity reaches a critical point and as n to an exponent depending on the singularity be...
متن کاملEmbeddings of Schatten Norms with Applications to Data Streams
Given an n×d matrix A, its Schatten-p norm, p ≥ 1, is defined as ‖A‖p = (∑rank(A) i=1 σi(A) p )1/p , where σi(A) is the i-th largest singular value of A. These norms have been studied in functional analysis in the context of non-commutative `p-spaces, and recently in data stream and linear sketching models of computation. Basic questions on the relations between these norms, such as their embed...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Cybernetics
سال: 2020
ISSN: 2168-2267,2168-2275
DOI: 10.1109/tcyb.2020.3004437