Difference between revisions of "Local Linear Embedding (LLE)"

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* [http://cs.nyu.edu/~roweis/lle/ Locally Linear Embedding | S.T. Roweis & L. K. Saul - NYU]
 
* [http://cs.nyu.edu/~roweis/lle/ Locally Linear Embedding | S.T. Roweis & L. K. Saul - NYU]
 
* [http://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction Nonlinear  dimensionality reduction | Wikipedia]
 
* [http://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction Nonlinear  dimensionality reduction | Wikipedia]
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Embeddings...
 
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* projecting an input into another more convenient representation space. For example we can project (embed) faces into a space in which face matching can be more reliable. | [http://www.quora.com/profile/Chomba-Bupe Chomba Bupe]
 
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* a mapping of a discrete — categorical — variable to a vector of continuous numbers. In the context of neural networks, embeddings are low-dimensional, learned continuous vector representations of discrete variables. Neural network embeddings are useful because they can reduce the dimensionality of categorical variables and meaningfully represent categories in the transformed space. [http://towardsdatascience.com/neural-network-embeddings-explained-4d028e6f0526 Neural Network Embeddings Explained | Will Koehrsen - Towards Data Science]
 
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* a relatively low-dimensional space into which you can translate high-dimensional vectors. Embeddings make it easier to do machine learning on large inputs like sparse vectors representing words. Ideally, an embedding captures some of the semantics of the input by placing semantically similar inputs close together in the embedding space. An embedding can be learned and reused across models. [http://developers.google.com/machine-learning/crash-course/embeddings/video-lecture Embeddings | Machine Learning Crash Course]
 
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Neural network embeddings have 3 primary purposes:
 
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# Finding nearest neighbors in the embedding space. These can be used to make recommendations based on user interests or cluster categories.
 
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# As input to a machine learning model for a supervised task.
 
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# For visualization of concepts and relations between categories.
 
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begins by finding a set of the nearest neighbors of each point. It then computes a set of weights for each point that best describes the point as a linear combination of its neighbors. Finally, it uses an [http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors]-based optimization technique to find the low-dimensional embedding of points, such that each point is still described with the same linear combination of its neighbors. LLE tends to handle non-uniform sample densities poorly because there is no fixed unit to prevent the weights from drifting as various regions differ in sample densities. LLE has no internal model. LLE was presented at approximately the same time as Isomap. It has several advantages over Isomap, including faster optimization when implemented to take advantage of sparse matrix algorithms, and better results with many problems
 
begins by finding a set of the nearest neighbors of each point. It then computes a set of weights for each point that best describes the point as a linear combination of its neighbors. Finally, it uses an [http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors]-based optimization technique to find the low-dimensional embedding of points, such that each point is still described with the same linear combination of its neighbors. LLE tends to handle non-uniform sample densities poorly because there is no fixed unit to prevent the weights from drifting as various regions differ in sample densities. LLE has no internal model. LLE was presented at approximately the same time as Isomap. It has several advantages over Isomap, including faster optimization when implemented to take advantage of sparse matrix algorithms, and better results with many problems

Revision as of 09:34, 5 April 2020

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begins by finding a set of the nearest neighbors of each point. It then computes a set of weights for each point that best describes the point as a linear combination of its neighbors. Finally, it uses an [1]-based optimization technique to find the low-dimensional embedding of points, such that each point is still described with the same linear combination of its neighbors. LLE tends to handle non-uniform sample densities poorly because there is no fixed unit to prevent the weights from drifting as various regions differ in sample densities. LLE has no internal model. LLE was presented at approximately the same time as Isomap. It has several advantages over Isomap, including faster optimization when implemented to take advantage of sparse matrix algorithms, and better results with many problems

Steps-of-locally-linear-embedding-algorithm.png


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