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68
MultiScale Clustering by Building a Robust and Self Correcting Ultrametric Topology on Data Points
"... The advent of highthroughput technologies and the concurrent advances in information sciences have led to an explosion in size and complexity of the data sets collected in biological sciences. The biggest challenge today is to assimilate this wealth of information into a conceptual framework that w ..."
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. This hierarchy is then transformed into an ultrametric space, which is then represented via an ultrametric tree or a Parisi matrix. Secondly, it has a builtin mechanism for selfcorrecting clustering membership across different tree levels. We have compared the trees generated with this new algorithm
A note on local ultrametricity in text
 http://arxiv.org/pdf/cs.CL/0701181, 2007. 13 F. Murtagh, Correspondence Analysis and Data Coding with R and Java, Chapman & Hall/CRC
, 2005
"... High dimensional, sparsely populated data spaces have been characterized in terms of ultrametric topology. This implies that there are natural, not necessarily unique, tree or hierarchy structures defined by the ultrametric topology. In this note we study the extent of local ultrametric topology in ..."
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Cited by 2 (2 self)
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High dimensional, sparsely populated data spaces have been characterized in terms of ultrametric topology. This implies that there are natural, not necessarily unique, tree or hierarchy structures defined by the ultrametric topology. In this note we study the extent of local ultrametric topology
Ultrametric Watersheds
, 2009
"... We study hierachical segmentation in the framework of edgeweighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical edgesegmentations. Sep 2011 ..."
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Cited by 7 (6 self)
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We study hierachical segmentation in the framework of edgeweighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical edgesegmentations. Sep 2011
Ultrametric Model of Mind, I: Review
, 2013
"... We mathematically model Ignacio Matte Blanco’s principles of symmetric and asymmetric being through use of an ultrametric topology. We use for this the highly regarded 1975 book of this Chilean psychiatrist and pyschoanalyst (born 1908, died 1995). Such an ultrametric model corresponds to hierarch ..."
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We mathematically model Ignacio Matte Blanco’s principles of symmetric and asymmetric being through use of an ultrametric topology. We use for this the highly regarded 1975 book of this Chilean psychiatrist and pyschoanalyst (born 1908, died 1995). Such an ultrametric model corre
Ultrametric and Generalized Ultrametric in Logic and in Data Analysis
, 2010
"... Following a review of metric, ultrametric and generalized ultrametric, we review their application in data analysis. We show how they allow us to explore both geometry and topology of information, starting with measured data. Some themes are then developed based on the use of metric, ultrametric and ..."
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Cited by 1 (1 self)
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Following a review of metric, ultrametric and generalized ultrametric, we review their application in data analysis. We show how they allow us to explore both geometry and topology of information, starting with measured data. Some themes are then developed based on the use of metric, ultrametric
Alexandroff and Scott Topologies for Generalized Ultrametric Spaces
, 1995
"... Both preorders and ordinary ultrametric spaces are instances of generalized ultrametric spaces. Every generalized ultrametric space can be isometrically embedded in a (complete) function space by means of an ultrametric version of the categorical Yoneda Lemma. This simple fact gives naturally ris ..."
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rise to: 1. a topology for generalized ultrametric spaces which for arbitrary preorders corresponds to the Alexandroff topology and for ordinary ultrametric spaces reduces to the fflball topology; 2. a topology for algebraic complete generalized ultrametric spaces generalizing both the Scott
Semiparametric Estimation of (Constrained) Ultrametric Trees
, 1996
"... This paper is concerned with the semiparametric estimation of Ultrametric treerepresentations of subjects ' paired comparisons of stimuli, and captures subject heterogeneity using a finite mixture formulation. In many other approaches to the analysis of subjects decision processes, such finit ..."
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This paper is concerned with the semiparametric estimation of Ultrametric treerepresentations of subjects ' paired comparisons of stimuli, and captures subject heterogeneity using a finite mixture formulation. In many other approaches to the analysis of subjects decision processes
Generalized Ultrametric Spaces: Completion, Topology, and Powerdomains via the Yoneda Embedding
, 1995
"... ..."
A COMMON GENERALIZATION OF METRIC, ULTRAMETRIC AND TOPOLOGICAL FIXED POINT THEOREMS
"... Abstract. We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach’s Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not involving any metrics. We demonstrate its applications to ..."
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Abstract. We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach’s Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not involving any metrics. We demonstrate its applications
On the ultrametric StoneWeierstrass theorem and Mahler’s expansion
, 2004
"... We describe an ultrametric version of the StoneWeierstrass theorem, without any assumption on the residue field. If E is a subset of a rankone valuation domain V, we show that the ring of polynomial functions is dense in the ring of continuous functions from E to V if and only if the topological ..."
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Cited by 4 (2 self)
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We describe an ultrametric version of the StoneWeierstrass theorem, without any assumption on the residue field. If E is a subset of a rankone valuation domain V, we show that the ring of polynomial functions is dense in the ring of continuous functions from E to V if and only if the topological
Results 1  10
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68