Soft memberships for spectral clustering, with application to permeable language distinction

Nock, Richard; Vaillant, Pascal; Henry, Claudia; Nielsen, Frank

doi:10.1016/j.patcog.2008.06.024

Cited by 8 publications

(5 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case of spectral partitioning, this may be done by replacing the hard k -means subroutine with a Gaussian mixture model or by using more advanced methods, such as those in ref. 32.…”

Section: Discussionmentioning

confidence: 99%

Structure and information in spatial segregation

Chodrow

2017

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

Ethnoracial residential segregation is a complex, multiscalar phenomenon with immense moral and economic costs. Modeling the structure and dynamics of segregation is a pressing problem for sociology and urban planning, but existing methods have limitations. In this paper, we develop a suite of methods, grounded in information theory, for studying the spatial structure of segregation. We first advance existing profile and decomposition methods by posing two related regionalization methods, which allow for profile curves with nonconstant spatial scale and decomposition analysis with nonarbitrary areal units. We then formulate a measure of local spatial scale, which may be used for both detailed, within-city analysis and intercity comparisons. These methods highlight detailed insights in the structure and dynamics of urban segregation that would be otherwise easy to miss or difficult to quantify. They are computationally efficient, applicable to a broad range of study questions, and freely available in open source software.

show abstract

“…In the case of spectral partitioning, this may be done by replacing the hard k -means subroutine with a Gaussian mixture model or by using more advanced methods, such as those in ref. 32.…”

Section: Discussionmentioning

confidence: 99%

Structure and information in spatial segregation

Chodrow

2017

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…We use the set of trajectories {x i (t)} 1≤i≤N to partition the spatial domain into clusters. The spectral clustering algorithm performs an eigenanalysis to project the trajectory set onto a subspace that may yield clusters maximizing the within-cluster similarity and minimizing the between-clusters similarity [41]. Particles clustered together should move as a compact group, with limited mixing with particles outside of the cluster, while particles in different clusters should experience dissimilar trajectories [5,15].…”

Section: Spectral Clustering Methods With Soft Memberships For Trajec...mentioning

confidence: 99%

Uncertainty Quantification of Trajectory Clustering Applied to Ocean Ensemble Forecasts

Vieira

Rypina

Allshouse

2020

Fluids

View full text Add to dashboard Cite

Partitioning ocean flows into regions dynamically distinct from their surroundings based on material transport can assist search-and-rescue planning by reducing the search domain. The spectral clustering method partitions the domain by identifying fluid particle trajectories that are similar. The partitioning validity depends on the accuracy of the ocean forecasting, which is subject to several sources of uncertainty: model initialization, limited knowledge of the physical processes, boundary conditions, and forcing terms. Instead of a single model output, multiple realizations are produced spanning a range of potential outcomes, and trajectory clustering is used to identify robust features and quantify the uncertainty of the ensemble-averaged results. First, ensemble statistics are used to investigate the cluster sensitivity to the spectral clustering method free-parameters and the forecast parameters for the analytic Bickley jet, a geostrophic flow model. Then, we analyze an operational coastal ocean ensemble forecast and compare the clustering results to drifter trajectories south of Martha’s Vineyard. This approach identifies regions of low uncertainty where drifters released within a cluster predominantly remain there throughout the window of analysis. Drifters released in regions of high uncertainty tend to either enter neighboring clusters or deviate from all predicted outcomes.

show abstract

“…We use the set of trajectories {x i (t)} 1≤i≤N to partition the spatial domain into clusters. The spectral clustering algorithm performs an eigenanalysis to project the trajectory set onto a subspace that may yield clusters maximizing the within-cluster similarity and minimizing the between-clusters similarity [Nock et al, 2009]. Particles clustered together should move as a compact group, with limited mixing with particles outside of the cluster, while particles in different clusters should experience dissimilar trajectories [Froyland and Padberg-Gehle, 2015;Hadjighasem et al, 2016].…”

Section: Spectral Clustering Methods With Soft Memberships For Trajec...mentioning

confidence: 99%

Uncertainty Quantification of Trajectory Clustering Applied to Ocean Ensemble Forecasts

Vieira¹,

Rypina²,

Allshouse³

2020

Preprint

View full text Add to dashboard Cite

Partitioning ocean flows into regions dynamically distinct from their surroundings based on material transport can assist search-and-rescue planning by reducing the search domain. The spectral clustering method partitions the domain by identifying fluid particle trajectories that are similar. The partitioning validity depends on the accuracy of the ocean forecasting, which is subject to several sources of uncertainty: model initialization, limited knowledge of the physical processes, boundary conditions, and forcing terms. Instead of a single model output, multiple realizations are produced spanning a range of potential outcomes, and trajectory clustering is used to identify robust features and quantify the uncertainty of the ensemble-averaged results. First, ensemble statistics are used to investigate the cluster sensitivity to the spectral clustering method free-parameters and the forecast parameters for the analytic Bickley jet, a geostrophic flow model. Then, we analyze an operational coastal ocean ensemble forecast and compare the clustering results to drifter trajectories south of Martha's Vineyard. This approach accurately identifies regions of low uncertainty where drifters released within a cluster remain there throughout the window of analysis. Drifters released in regions of high uncertainty tend to either enter neighboring clusters or deviate from all predicted outcomes.

show abstract

Soft memberships for spectral clustering, with application to permeable language distinction

Cited by 8 publications

References 7 publications

Structure and information in spatial segregation

Structure and information in spatial segregation

Uncertainty Quantification of Trajectory Clustering Applied to Ocean Ensemble Forecasts

Uncertainty Quantification of Trajectory Clustering Applied to Ocean Ensemble Forecasts

Contact Info

Product

Resources

About