t_sne_isomap.tns
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: Dinho_Darroz
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.49 Ko KB
Mis en ligne Uploaded: 18/06/2024 - 10:03:11
Mis à jour Updated: 18/06/2024 - 10:04:48
Uploadeur Uploader: Dinho_Darroz (Profil)
Téléchargements Downloads: 3
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4080977
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.49 Ko KB
Mis en ligne Uploaded: 18/06/2024 - 10:03:11
Mis à jour Updated: 18/06/2024 - 10:04:48
Uploadeur Uploader: Dinho_Darroz (Profil)
Téléchargements Downloads: 3
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4080977
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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t-Distributed Stochastic Neighbor Embedding (t-SNE) Overview t-SNE is a non-linear dimensionality reduction technique that is particularly well suited for embedding high-dimensional data into a space of two or three dimensions for visualization. Key Concepts High-Dimensional Similarity : Measures how similar points are in high-dimensional space. Low-Dimensional Similarity : Measures how similar points are in the low-dimensional embedding. KL Divergence : Measures the difference between high-dimensional and low-dimensional similarities. Steps Compute Pairwise Similarities in High Dimensions : Use a Gaussian distribution to measure the similarity between points. The similarity between points xix_i x i and xjx_j x j is given by: pij=expa(%xixj%2/2Ãi2)k`lexpa(%xkxl%2/2Ãk2)p_{ij} = frac{exp(-|x_i - x_j|^2 / 2sigma_i^2)}{sum_{k neq l} exp(-|x_k - x_l|^2 / 2sigma_k^2)} p ij = k = l exp ( % x k x l % 2 /2 Ã k 2 ) exp ( % x i x j % 2 /2 Ã i 2 ) Compute Pairwise Similarities in Low Dimensions : Use a Student-t distribution with one degree of freedom (Cauchy distribution). The similarity between points yiy_i y i and yjy_j y j in low dimensions is given by: qij=(1+%yiyj%2)1k`l(1+%ykyl%2)1q_{ij} = frac{(1 + |y_i - y_j|^2)^{-1}}{sum_{k neq l} (1 + |y_k - y_l|^2)^{-1}} q ij = k = l ( 1 + % y k y l % 2 ) 1 ( 1 + % y i y j % 2 ) 1 Minimize KL Divergence : Use gradient descent to minimize the Kullback-Leibler divergence between the distributions PP P and QQ Q : KL(P%Q)=i`jpijlogapijqijKL(P | Q) = sum_{i neq j} p_{ij} log frac{p_{ij}}{q_{ij}} K L ( P % Q ) = i = j p ij lo g q ij p ij Applications Visualization of high-dimensional data (e.g., images, text, and genomics data). Stochastic Neighbor Embedding (SNE) Overview SNE is a precursor to t-SNE and is also used for dimensionality reduction, focusing on preserving neighborhood structures in the data. Key Concepts Probability Distributions : Similar to t-SNE, but both high-dimensional and low-dimensional similarities are modeled with Gaussian distributions. KL Divergence : Used to measure the difference between the high-dimensional and low-dimensional similarities. Steps Compute Pairwise Similarities in High Dimensions : Use a Gaussian distribution to measure the similarity between Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
t-Distributed Stochastic Neighbor Embedding (t-SNE) Overview t-SNE is a non-linear dimensionality reduction technique that is particularly well suited for embedding high-dimensional data into a space of two or three dimensions for visualization. Key Concepts High-Dimensional Similarity : Measures how similar points are in high-dimensional space. Low-Dimensional Similarity : Measures how similar points are in the low-dimensional embedding. KL Divergence : Measures the difference between high-dimensional and low-dimensional similarities. Steps Compute Pairwise Similarities in High Dimensions : Use a Gaussian distribution to measure the similarity between points. The similarity between points xix_i x i and xjx_j x j is given by: pij=expa(%xixj%2/2Ãi2)k`lexpa(%xkxl%2/2Ãk2)p_{ij} = frac{exp(-|x_i - x_j|^2 / 2sigma_i^2)}{sum_{k neq l} exp(-|x_k - x_l|^2 / 2sigma_k^2)} p ij = k = l exp ( % x k x l % 2 /2 Ã k 2 ) exp ( % x i x j % 2 /2 Ã i 2 ) Compute Pairwise Similarities in Low Dimensions : Use a Student-t distribution with one degree of freedom (Cauchy distribution). The similarity between points yiy_i y i and yjy_j y j in low dimensions is given by: qij=(1+%yiyj%2)1k`l(1+%ykyl%2)1q_{ij} = frac{(1 + |y_i - y_j|^2)^{-1}}{sum_{k neq l} (1 + |y_k - y_l|^2)^{-1}} q ij = k = l ( 1 + % y k y l % 2 ) 1 ( 1 + % y i y j % 2 ) 1 Minimize KL Divergence : Use gradient descent to minimize the Kullback-Leibler divergence between the distributions PP P and QQ Q : KL(P%Q)=i`jpijlogapijqijKL(P | Q) = sum_{i neq j} p_{ij} log frac{p_{ij}}{q_{ij}} K L ( P % Q ) = i = j p ij lo g q ij p ij Applications Visualization of high-dimensional data (e.g., images, text, and genomics data). Stochastic Neighbor Embedding (SNE) Overview SNE is a precursor to t-SNE and is also used for dimensionality reduction, focusing on preserving neighborhood structures in the data. Key Concepts Probability Distributions : Similar to t-SNE, but both high-dimensional and low-dimensional similarities are modeled with Gaussian distributions. KL Divergence : Used to measure the difference between the high-dimensional and low-dimensional similarities. Steps Compute Pairwise Similarities in High Dimensions : Use a Gaussian distribution to measure the similarity between Made with nCreator - tiplanet.org
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