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**K**-**Medoids**: Instead of taking the mean value of the object in a cluster as a reference point, **medoids** can be used, which is the most centrally located object in a cluster. The **K**-**Medoids** Clustering Method Find representative objects, ...

**K**-**Medoids**: Instead of taking the mean value of the object in a cluster as a reference point, **medoids** can be used, which is the most centrally located object in a cluster. Fuzzy C-means Clustering Fuzzy c-means (FCM) ...

4. Clustering Methods Concepts Partitional (**k**-Means, **k**-**Medoids**) Hierarchical (Agglomerative & Divisive, COBWEB) Density-based (DBSCAN, CLIQUE) Large size data (STING, BIRCH, CURE)

**K**-**Medoids**: Instead of taking the mean value of the object in a cluster as a reference point, **medoids** can be used, which is the most centrally located object in a cluster. 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10

... in advance Unable to handle noisy data and outliers Not suitable to discover clusters with non-convex shapes The **K**-**Medoids** Clustering Method Find representative objects, called **medoids**, in clusters PAM (Partitioning Around **Medoids**, ...

Overview Of Clustering Techniques D. Gunopulos, UCR Clusteting Data Clustering Algorithms **K**-means and **K**-**medoids** algorithms Density Based algorithms Density Approximation Spatial Association Rules (Koperski et al, 95) Statistical techniques (Wang et al, 1997) Finding proximity relationships ...

Only 1 minimum (mean of data set) We need cut-off **K**-**medoids** cut-off depends on cluster centers Cluster center independent cut-off? Gaussian function! Is DENCLUE only an Approximation to **k**-**medoids**?

... new dissimilarity measures to deal with categorical objects Using a frequency based method to update modes of clusters **k**-**Medoids** clustering method **k**-Means algorithm is sensitive to outliers Since an object with an extremely large value may substantially distort the distribution of the data.

Determining **k** Trial and error X-means, PCA-based Crisp clustering EM, Fuzzy c-means Should not be confused with **k**-NN **k**-**Medoids** Medoid – the most centrally located point in a cluster, as a representative point of the cluster.

The E step can modified to have a general dissimilarity measure which leads to the **K**-**medoids** algorithm. Can speed up **K**-means through various methods: Pre-compute a tree where near by points are in the same sub tree. (Ramas. And Paliwal, 1990) Use ...

PAM (Partitioning Around **Medoids**, 1987) Choose randomly **k** **medoids** from the original dataset X Assign each of the n-**k** remaining points in X to their closest medoid iteratively replace one of the **medoids** by one of the non-**medoids** if it improves the total clustering cost Discussion of PAM ...

**k**-Means (and EM), **k**-**Medoids**. Hierarchical methods. agglomerative, divisive, BIRCH. Model-based clustering methods. Properties of Vector Similarity as a distance measure for text clusterings. Similarity between a doc and the centroid is equal to.

Since an object with an extremely large value may substantially distort the distribution of the data **K**-**Medoids**: Instead of taking the mean value of the object in a cluster as a reference point, **medoids** can be used, ...

Capture differences between objective functions similar to **k**-means (ex. **k**-medians, **k**-**medoids**, min-sum) Show bounds on the size of the Range of weight considering and weight sensitive methods

Assume we apply **K**-**medoids** for **k**=3 to a dataset consisting of 5 objects numbered 1,..5 with the following distance matrix: The current set of representatives is {1,3,4}; indicate all computations **k**-**medoids** (PAM) performs in its next iteration. Distance Matrix:

... in advance Unable to handle noisy data and outliers Not suitable to discover clusters with non-convex shapes The **K**-**Medoids** Clustering Method Find representative objects, called **medoids**, in clusters PAM (Partitioning Around **Medoids**, ...

**K**-**medoids** Clustering Each center is represented by one of the objects (representative objects, called **medoids**) in the cluster. 1) The algorithm begins with arbitrary selection of the **k** objects as medoid points out of n data points (n>**k**) 2) ...

Assess cluster structure for fit and stability **K**-**medoids** A little different Centroid: The average of the samples within a cluster Medoid: The “representative object” within a cluster. Initializing requires choosing **medoids** at random. 7.

... in advance Unable to handle noisy data and outliers Not suitable to discover clusters with non-convex shapes The **K**-**Medoids** Clustering Method Find representative objects, called **medoids**, in clusters PAM (Partitioning Around **Medoids**, ...

... **k**-prototype method DBMiner Examples Show help on clustering Show examples The **K**-**Medoids** Clustering Method Find representative objects, called **medoids**, in clusters PAM (Partitioning Around **Medoids**, 1987) ...

Since an object with an extremely large value may substantially distort the distribution of the data **K**-**Medoids**: Instead of taking the mean value of the object in a cluster as a reference point, **medoids** can be used, ...

... The Number of Features The Number of Class Synthetic 2000 2 3 FUZZY C-MEANS ALGORITHM EXAMPLE C=3 m=5 ε=1e-6 Results **K**-**MEDOIDS** is the best algorithm according to **K**-MEANS and FUZZY C-MEANS. However, **K**-**MEDOIDS** algorithm is suitable for small datasets.

**K**-means and **K**-**medoids** Partitioning Method Don’t get pretty picture MUST choose number of clusters **K** a priori More of a “black box” because output is most commonly looked at purely as assignments Each object (gene or sample) ...

**K**-means **K**-**medoids** Density Based Clustering centering on DBSCAN Region Discovery and CLEVER Side discussions on Project2 and Project3. Special Dates: Labs: Sept. 1, Sept. 22;Discussion Project 2: September 15;Review: Sept. 29 (questions will be posted Sept. 23), ...

... the clustering results based on personalized ranking and reranking Progress Implemented two clustering algorithms **K**-**Medoids** Hierarchical clustering Presentation Replace Google ads with clustering results Present ranked results together with clustering results Two presentation strategies ...

Clustering Summary unsupervised many approaches **K**-means – simple, sometimes useful **K**-**medoids** is less sensitive to outliers Hierarchical clustering – works for symbolic attributes Evaluation is a problem Clustering Outline Introduction **K**-means clustering Hierarchical clustering: ...

Public Cluster 1 of 3 DAF Standardized Mean Profile Cluster 1 of 3 from **K**-**Medoids** Algorithm Applied to the Top 400 Genes from the Two-Color Array Data Public Cluster 2 of 3 DAF Standardized Mean Profile Cluster 2 of 3 from **K**-**Medoids** Algorithm Applied to the Top 400 Genes from the Two-Color ...

Classical clustering methods Partitioning methods **k**-Means (and EM), **k**-**Medoids** Hierarchical methods agglomerative, divisive, BIRCH Model-based clustering methods **K**-means Works when we know **k**, the number of clusters we want to find Idea: ...

Use **K**-**medoids**. Add definition of median . **K**-means. Disadvantages. Dependent on initialization. Sensitive to outliers (**K**-**medoids**) Can deal only with clusters with spherical symmetrical point distribution. Kernel trick. **K**-means. Disadvantages. Dependent on initialization.

... Using a frequency-based method to update modes of clusters Handling a mixture of categorical and numerical data: **k**-prototype method The **K**-**Medoids** Clustering Method Find representative objects, called **medoids**, in clusters PAM ...

... we used **K**-**medoids** Easier to use in a proof of concept Our **k**-**medoids** implementation is serial Can easily be converted to **K**-means by image-segmentation developers without parallel computing experience Randomly picks starting **medoids** and runs **k**-**medoids** algorithm multiple times Image ...

... S1 S2| = **k** - 1 each node has **k**(n-**k**) neighbors each node represent a collection of **k** **medoids**, each node corresponds to a clustering (dynamic) draws a sample of neighbors in each step of a search if a better neighbor is found, moves to the neighbor’s node CLARANS Two parameters: ...

**K**-**medoids** is more robust than **k**-means in presence of noise and outliers. **K**-means is less costly in terms of processing time. Fuzzy C-means Fuzzy C-means Fuzzy version of **K**-means Elements may belong to more than one cluster Values of characteristic function range from 0 to 1.

**K**-**Medoids**: Instead of taking the mean value of the object in a cluster as a reference point, **medoids** can be used, which is the most centrally located object in a cluster. The **K**-**Medoids** Clustering Method Find representative objects, ...

**K**-**Medoids**: Instead of taking the mean value of the object in a cluster as a reference point, **medoids** can be used, which is the most centrally located object in a cluster.

... Bayesian classifiers Decision tree methods Decision rules methods Classifier evaluation techniques Clustering methods **K**-means and **K**-**medoids** algorithms Hierarchical clustering Density clustering Summary „Data mining” Vietnam national university in Hanoi, ...

* Clustering Summary unsupervised many approaches **K**-means – simple, sometimes useful **K**-**medoids** is less sensitive to outliers Hierarchical clustering – works for symbolic attributes Evaluation is a problem * * * * Outline Introduction **K**-means clustering Hierarchical clustering: ...

1 2 3 4 5 6 7 8 9 10 When **k** = 1, ... Step 5 Comments on the **K**-Means Method The **K**-**Medoids** Clustering Method Slide 65 Slide 66 Slide 67 Slide 68 Slide 69 Slide 70 Slide 71 Slide 72 Slide 73 Slide 74 Slide 75 Slide 76 Partitional Clustering Algorithms Partitional Clustering Algorithms ...

... a set of **k** **medoids** If the local optimum is found, CLARANS starts with new randomly selected node in search for a new local optimum It is more efficient and scalable than both PAM and CLARA Focusing techniques and spatial access structures may further improve its performance ...

The **K**-**Medoids** Clustering Method A Typical **K**-**Medoids** Algorithm (PAM) PAM (Partitioning Around **Medoids**) (1987) PAM Clustering: Total swapping cost TCih= jCjih A **Medoids** Clustering Example Calculate Cost: ...

Clustering Summary unsupervised many approaches **K**-means – simple, sometimes useful **K**-**medoids** is less sensitive to outliers Hierarchical clustering – works for symbolic attributes Evaluation is a problem Clustering Outline Introduction **K**-means clustering Hierarchical clustering: ...

... **K**-**medoids** Error vs. Number of Views Human body configurations Automatically Locating Keypoints Results Trademark Similarity Outline Mori, Belongie, Malik (CVPR 01) Representative Shape Contexts Snodgrass Results Results Conclusion ...

... **K**-centers clustering (aka **K**-**medoids** clustering and **K**-medians clustering) Randomly choose initial exemplars, (data centers) **K**-centers clustering (aka **K**-**medoids** clustering and **K**-medians clustering) Assign data points to nearest centers **K**-centers clustering ...

**K**-Route Diversification CSci 5980 - Team 6 ... Cluster routes into **k** clusters and select a prototype for each cluster using **k**-**medoids** Employing Minack diversity algorithm by adapting an existing objective function Defining a diversity measure for this problem ...

Title: **K**-means Clustering Author: Nilanjan Ray Last modified by: nray1 Created Date: 10/14/2008 8:55:43 PM Document presentation format: On-screen Show (4:3)

**K** – Means, **K** – **Medoids**, Fuzzy. Measure of distance – but do not need to compute full distance matrix. Specify number of groups in advance. Minimizing within group variability. Finds spherical clusters. Procedure. Start with centers for **k** groups (user-supplied or random)

**K**-**Medoids**: Instead of taking the mean value of the object in a cluster as a reference point, **medoids** can be used, which is the most centrally located object in a cluster.

... … (Web pages containing the descriptions of the topic) Naïve bayes … … Clustering Hierarchical Partitioning **K**-means ... “There are many clustering techniques (e.g., hierarchical, partitioning, **k**-means, **k**-**medoids**).” CS583, Bing Liu * Put them together Crawl the ...

Use a **k**-**medoids** algorithm (see below), where a cluster is represented by one of its points. Drawback 4: **k**-means is not suitable for data with nominal (categorical) coordinates. Strategies for facing drawback 4: Use a **k**-**medoids** algorithm. Hard ...

... Similarity Matrix Document Clustering Techniques Document Clustering Techniques Some Clustering Methods **K**-Means **K**-means and **K**-**medoids** algorithms **K**-Means Clustering Slide 29 Slide 30 Slide 31 Slide 32 Slide 33 Question Problems with **K**-means type algorithms Agglomerative Clustering ...