Kmeans
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: Dinho_Darroz
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.28 Ko KB
Mis en ligne Uploaded: 18/06/2024 - 08:16:28
Mis à jour Updated: 18/06/2024 - 08:31:16
Uploadeur Uploader: Dinho_Darroz (Profil)
Téléchargements Downloads: 7
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4080743
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.28 Ko KB
Mis en ligne Uploaded: 18/06/2024 - 08:16:28
Mis à jour Updated: 18/06/2024 - 08:31:16
Uploadeur Uploader: Dinho_Darroz (Profil)
Téléchargements Downloads: 7
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4080743
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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Here's a step-by-step explanation of how K-means works: Initialization : Select kk k initial centroids randomly from the dataset. These centroids represent the initial cluster centers. Assignment Step : Assign each data point to the nearest centroid. This creates kk k clusters based on the proximity of data points to the centroids. Update Step : Recalculate the centroids by computing the mean of all data points assigned to each cluster. Repeat : Repeat the assignment and update steps until the centroids no longer change significantly or a predetermined number of iterations is reached. Optimization Criterion in K-Means The optimization criterion in K-means is to minimize the within-cluster sum of squares (WCSS), also known as the sum of squared errors (SSE). This criterion can be expressed as: WCSS = i = 1 k x C i % x ¼ i % 2 K-means++ Initialization K-means++ is an enhancement of the K-means algorithm that improves the initialization of the centroids, leading to better convergence. Algorithm: Choose the first centroid : Randomly select the first centroid from the data points. Choose the remaining centroids : For each remaining centroid, select a data point xx x with a probability proportional to the square of its distance to the nearest existing centroid. Specifically, for each data point xx x , compute the distance D(x)D(x) D ( x ) to the nearest centroid already chosen, and then select a new centroid from the data points with a probability proportional to D(x)2D(x)^2 D ( x ) 2 . Proceed with K-means : Once the initial centroids are chosen, proceed with the standard K-means algorithm (assignment and update steps). Pros and Cons: Pros : Leads to better clustering results, reduces the chance of poor initialization. Cons : Slightly more computationally expensive during initialization compared to standard K-means. Summary K-means is simple and fast but sensitive to initialization and not robust to outliers. K-medians is more robust to outliers and uses Manhattan distance but is computationally more expensive. K-means++ improves the initialization process of K-means, leading to better convergence and clustering results. These variations provide different approaches to clustering, with trade-offs between robustness, computational complexity, and sensitivity to initialization. Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
Here's a step-by-step explanation of how K-means works: Initialization : Select kk k initial centroids randomly from the dataset. These centroids represent the initial cluster centers. Assignment Step : Assign each data point to the nearest centroid. This creates kk k clusters based on the proximity of data points to the centroids. Update Step : Recalculate the centroids by computing the mean of all data points assigned to each cluster. Repeat : Repeat the assignment and update steps until the centroids no longer change significantly or a predetermined number of iterations is reached. Optimization Criterion in K-Means The optimization criterion in K-means is to minimize the within-cluster sum of squares (WCSS), also known as the sum of squared errors (SSE). This criterion can be expressed as: WCSS = i = 1 k x C i % x ¼ i % 2 K-means++ Initialization K-means++ is an enhancement of the K-means algorithm that improves the initialization of the centroids, leading to better convergence. Algorithm: Choose the first centroid : Randomly select the first centroid from the data points. Choose the remaining centroids : For each remaining centroid, select a data point xx x with a probability proportional to the square of its distance to the nearest existing centroid. Specifically, for each data point xx x , compute the distance D(x)D(x) D ( x ) to the nearest centroid already chosen, and then select a new centroid from the data points with a probability proportional to D(x)2D(x)^2 D ( x ) 2 . Proceed with K-means : Once the initial centroids are chosen, proceed with the standard K-means algorithm (assignment and update steps). Pros and Cons: Pros : Leads to better clustering results, reduces the chance of poor initialization. Cons : Slightly more computationally expensive during initialization compared to standard K-means. Summary K-means is simple and fast but sensitive to initialization and not robust to outliers. K-medians is more robust to outliers and uses Manhattan distance but is computationally more expensive. K-means++ improves the initialization process of K-means, leading to better convergence and clustering results. These variations provide different approaches to clustering, with trade-offs between robustness, computational complexity, and sensitivity to initialization. Made with nCreator - tiplanet.org
>>
