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- Max Vladymyrov, Miguel Á. Carreira-Perpiñán
- ArXiv
- 2012

1 Abstract Stochastic neighbor embedding (SNE) and related nonlinear man-ifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding algorithms that includes SNE and other existing algorithms, and study their relation with spectral methods… (More)

- Max Vladymyrov, Miguel Á. Carreira-Perpiñán
- AISTATS
- 2014

Introduction. Dimensionality reduction is an important task in machine learning. It arrises when there is a need for exploratory analysis of a dataset, to reveal hidden structure of the data, or as a pre-processing step, by extracting low-dimensional features that are useful for nearest-neighbor retrieval, classification, search or other applications, in an… (More)

1 Abstract Gaussian affinities are commonly used in graph-based methods such as spectral clustering or nonlinear embedding. Hinton and Roweis (2003) introduced a way to set the scale individually for each point so that it has a distribution over neighbors with a desired perplexity, or effective number of neighbors. This gives very good affinities that adapt… (More)

- Max Vladymyrov, Miguel Á. Carreira-Perpiñán
- ECML/PKDD
- 2013

Spectral methods for manifold learning and clustering typically construct a graph weighted with affinities (e.g. Gaussian or shortest-path distances) from a dataset and compute eigenvectors of a graph Laplacian. With large datasets, the eigendecomposition is too expensive, and is usually approximated by solving for a smaller graph defined on a subset of the… (More)

Nonlinear embedding algorithms such as stochastic neighbor embedding do di-mensionality reduction by optimizing an objective function involving similarities between pairs of input patterns. The result is a low-dimensional projection of each input pattern. A common way to define an out-of-sample mapping is to optimize the objective directly over a parametric… (More)

Spectral methods for dimensionality reduction and clustering require solving an eigenproblem defined by a sparse affinity matrix. When this matrix is large, one seeks an approximate solution. The standard way to do this is the Nyström method, which first solves a small eigenproblem considering only a subset of landmark points, and then applies an… (More)

Introduction Dimensionality reduction algorithms have long been used either for exploratory analysis of a high-dimensional dataset, to reveal structure such as clustering, or as a preprocessing step, by extracting low-dimensional features that are useful for classification or other tasks. Here we focus on dimensionality reduction algorithms where a dataset… (More)

Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding algorithms that includes SNE and other existing algorithms, and study their relation with spectral methods and graph… (More)

- Max Vladymyrov, Miguel Á. Carreira-Perpiñán
- 2017 International Joint Conference on Neural…
- 2017

For problems of image or video segmentation, where clusters have a complex structure, a leading method is spectral clustering. It works by encoding the similarity between pairs of points into an affinity matrix and applying k-means in its low-order eigenspace, where the clustering structure is enhanced. When the number of points is large, an approximation… (More)

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