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A PHYSICS OF BOUNDED METRICS SPACES
, 1997
"... Abstract: We consider the possibility of obtaining emergent properties of physical spaces endowed with structures analogous to that of collective models put forward by classical statistical physics. We show that, assuming that a so called « metric scale » does exist, one can indeed recover a number ..."
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Abstract: We consider the possibility of obtaining emergent properties of physical spaces endowed with structures analogous to that of collective models put forward by classical statistical physics. We show that, assuming that a so called « metric scale » does exist, one can indeed recover a number
© Hindawi Publishing Corp. COMMON STATIONARY POINTS OF MULTIVALUED MAPPINGS ON BOUNDED METRIC SPACES
, 2000
"... Abstract. Necessary and sufficient conditions for the existence of common stationary points of two multivalued mappings and common stationary point theorems for multivalued mappings on bounded metric spaces are given. Our results extend the theorems due to Fisher in 1979, 1980, and 1983 and Ohta an ..."
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Abstract. Necessary and sufficient conditions for the existence of common stationary points of two multivalued mappings and common stationary point theorems for multivalued mappings on bounded metric spaces are given. Our results extend the theorems due to Fisher in 1979, 1980, and 1983 and Ohta
MML Identifier: TBSP_1. Totally Bounded Metric Spaces Alicia de la Cruz
"... and [14] provide the notation and terminology for this paper. For simplicity, we follow the rules: M denotes a non empty metric space, c denotes an element of M, N denotes a non empty metric structure, w denotes an element of N, G denotes a family of subsets of N, C denotes a subset of N, R denotes ..."
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and [14] provide the notation and terminology for this paper. For simplicity, we follow the rules: M denotes a non empty metric space, c denotes an element of M, N denotes a non empty metric structure, w denotes an element of N, G denotes a family of subsets of N, C denotes a subset of N, R denotes
MML Identifier:TBSP_1. Totally Bounded Metric Spaces Alicia de la Cruz
"... and [14] provide the notation and terminology for this paper. For simplicity, we follow the rules: M denotes a non empty metric space, c denotes an element of M, N denotes a non empty metric structure, w denotes an element of N, G denotes a family of subsets of N, C denotes a subset of N, R denotes ..."
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and [14] provide the notation and terminology for this paper. For simplicity, we follow the rules: M denotes a non empty metric space, c denotes an element of M, N denotes a non empty metric structure, w denotes an element of N, G denotes a family of subsets of N, C denotes a subset of N, R denotes
Mtree: An Efficient Access Method for Similarity Search in Metric Spaces
, 1997
"... A new access meth d, called Mtree, is proposed to organize and search large data sets from a generic "metric space", i.e. whE4 object proximity is only defined by a distance function satisfyingth positivity, symmetry, and triangle inequality postulates. We detail algorith[ for insertion o ..."
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Cited by 662 (38 self)
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A new access meth d, called Mtree, is proposed to organize and search large data sets from a generic "metric space", i.e. whE4 object proximity is only defined by a distance function satisfyingth positivity, symmetry, and triangle inequality postulates. We detail algorith[ for insertion
Searching in metric spaces
, 2001
"... The problem of searching the elements of a set that are close to a given query element under some similarity criterion has a vast number of applications in many branches of computer science, from pattern recognition to textual and multimedia information retrieval. We are interested in the rather gen ..."
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Cited by 434 (37 self)
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general case where the similarity criterion defines a metric space, instead of the more restricted case of a vector space. Many solutions have been proposed in different areas, in many cases without crossknowledge. Because of this, the same ideas have been reconceived several times, and very different
Gradient flows in metric spaces and in the space of probability measures
 LECTURES IN MATHEMATICS ETH ZÜRICH, BIRKHÄUSER VERLAG
, 2005
"... ..."
Distance metric learning, with application to clustering with sideinformation,”
 in Advances in Neural Information Processing Systems 15,
, 2002
"... Abstract Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as Kmeans initially fails to find one that is meaningful to a user, the only recourse may be for ..."
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Cited by 817 (13 self)
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be for the user to manually tweak the input space's metric until sufficiently good clusters are found. For these and other applications requiring good metrics, it is desirable that we provide a more systematic way for users to indicate what they consider "similar." For instance, we may ask them
Vol.2, No.4, September–October 1991 Université Catholique de Louvain Totally Bounded Metric Spaces MML Identifier: TBSP 1. Alicia
"... paper. For simplicity we follow the rules: M is a metric space, c, g are elements of the carrier of M, F is a family of subsets of the carrier of M, A, B are subsets of the carrier of M, f is a function, n, m, p, k are natural numbers, and r, s, L are real numbers. Next we state four propositions: ( ..."
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paper. For simplicity we follow the rules: M is a metric space, c, g are elements of the carrier of M, F is a family of subsets of the carrier of M, A, B are subsets of the carrier of M, f is a function, n, m, p, k are natural numbers, and r, s, L are real numbers. Next we state four propositions
A metric for distributions with applications to image databases
, 1998
"... We introduce a new distance between two distributions that we call the Earth Mover’s Distance (EMD), which reflects the minimal amount of work that must be performed to transform one distributioninto the other by moving “distribution mass ” around. This is a special case of the transportation proble ..."
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Cited by 438 (6 self)
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problem from linear optimization, for which efficient algorithms are available. The EMD also allows for partial matching. When used to compare distributions that have the same overall mass, the EMD is a true metric, and has easytocompute lower bounds. In this paper we focus on applications to image
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