Data Mining Cluster Analysis: Advanced Concepts And Algorith ✓ Solved

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Data Mining Cluster Analysis: Advanced Concepts and Algorithms

Hierarchical Clustering creates nested clusters. Agglomerative clustering algorithms vary in terms of how the proximity of two clusters is computed. The MIN (single link) method is susceptible to noise and outliers, while MAX/GROUP AVERAGE may not work well with non-globular clusters. The CURE algorithm attempts to mitigate these issues by utilizing a type of graph-based approach that uses a proximity matrix. CURE selects a constant number of points from a cluster and "shrinks" them toward the center, allowing for improved handling of clusters of varying shapes and sizes.

Graph-Based Clustering employs a proximity graph, where each point is treated as a node with weighted edges representing the proximity between nodes. Sparsification techniques in this context effectively reduce the amount of data processed, making clustering more efficient by maintaining only connections to the most similar neighboring points. This reduction can enhance clustering results by minimizing noise influence and delineating clusters more distinctly.

Chameleon is an advanced clustering method that employs dynamic modeling to observe similarities between clusters. It adapts to the unique characteristics of the data set, allowing for the identification of natural clusters. The algorithm uses interconnectivity and closeness to merge clusters based on shared properties, effectively maintaining self-similarity.

To implement these approaches, it is essential to handle various challenges in spatial data sets. Clusters must be identified as densely populated regions with different shapes and densities. Algorithms must require minimal supervision and be able to account for noise while effectively merging clusters based on dynamic relationships.

In clustering techniques like ROCK (RObust Clustering using linKs) for categorical and Boolean data, the algorithm assesses neighbors based on a similarity threshold, employing hierarchical methods for data grouping. Treatments of shared neighbors and link values are critical for clustering efficacy. Similarly, Jarvis-Patrick clustering utilizes a k-nearest neighbor approach to establish cluster membership based on shared neighbors, though it can suffer from brittleness if clusters do not meet specific thresholds.

A proposed solution involving the Shared Nearest Neighbor (SNN) algorithm involves computing a similarity matrix and selectively retaining the k most similar neighbors to create a sparsified similarity graph. Through this method, the algorithm can effectively identify core points and subsequently form clusters by determining the proximity of these key points. Discarding noise points allows for the refinement of clusters, which can be adapted for scenarios involving time series data and differing densities.

Paper For Above Instructions

Data mining encompasses a variety of techniques aimed at extracting meaningful patterns and knowledge from large sets of data. Among these techniques, cluster analysis serves a pivotal role by grouping data points into clusters that share similar characteristics. This paper explores advanced concepts and algorithms in cluster analysis, emphasizing hierarchical clustering, graph-based clustering, and the innovative Chameleon algorithm.

At its core, hierarchical clustering can be categorized into two main types: agglomerative and divisive. Agglomerative clustering begins with each data point as a separate cluster and progressively merges them based on proximity measures. However, traditional agglomerative methods such as the MIN or single link approach can suffer from sensitivity to noise and outliers (Tan, Steinbach & Kumar, 2006). The MAX or complete link method may further struggle with the identification of non-globular clusters, leading to inaccuracies in cluster formation.

To address these shortcomings, the CURE (Clustering Using Representatives) algorithm was introduced. CURE integrates a proximity matrix and minimizes the effects of noise by forming clusters around representative points that are adjusted or "shrunk" towards the cluster's centroid. This method increases resilience against outliers and enhances the algorithm's ability to manage clusters of variable shapes and sizes (Guha, Rastogi & Shim, 1998).

Building upon the concept of proximity, graph-based clustering models each data point as a node within a weighted graph. Edges denote similarities between nodes, enabling the algorithm to interpret clusters as connected components in the graph (Eddelbuettel, 2013). Sparsification techniques in graph-based clustering have demonstrated the ability to eliminate a significant majority of entries in a proximity matrix, allowing clustering algorithms to operate more efficiently and effectively. These methods connect only to the most similar neighbors, thereby improving the quality of clustering while mitigating the impact of noise (Karypis & Han, 2003).

The Chameleon algorithm further advances hierarchical clustering through dynamic modeling. This innovative approach emphasizes the adaptation of clustering to the characteristics observed in the dataset. The algorithm assesses relative interconnectivity and closeness between potential clusters, leading to more accurate merging of groups based on shared properties (Karypis, Han & Kumar, 1999). The dynamic nature of Chameleon underscores its potential to operate with minimal supervision, addressing the complexities of spatial data where clusters may vary in density and shape.

Chameleon begins with a preprocessing step to construct a k-nearest neighbor graph to identify relationships dynamically among points. This graph is then analyzed using a multilevel graph partitioning approach to generate numerous well-connected clusters that can later be refined through hierarchical agglomerative methods (Kumar & Raizada, 2013).

Another important clustering framework is ROCK, which emphasizes the presence of categorical and Boolean attributes in data. This algorithm implements hierarchical clustering by looking at thresholded relationships amongst neighbors, contributing to meaningful cluster formation (Khan & Ahmad, 2004). In contrast, the Jarvis-Patrick algorithm functions to identify clusters by evaluating mutual k-nearest neighbors, although it is not without limitations due to its susceptibility to rigidity and oversensitivity to threshold changes (Jarvis & Patrick, 1973).

An interesting approach worth mentioning is the Shared Nearest Neighbor (SNN) clustering, where a similarity matrix is calculated and sparsified to reveal significant connections between data points. This method identifies core points based on the density of shared neighbors while allowing noise to be discarded effectively (Ester et al., 1996). The complexity of SNN clustering highlights its challenges, notably the high computational requirements for nearest neighbor searches.

In conclusion, advanced cluster analysis techniques like CURE, Chameleon, ROCK, and SNN represent crucial developments in the field of data mining. Their respective methodologies provide enhanced capabilities for handling diverse datasets and optimizing clustering efficacy, ultimately contributing to the broader goal of knowledge extraction from complex and large-scale data.

References

  • Eddelbuettel, D. (2013). Seamless R and C++ integration using Rcpp. Springer Science & Business Media.
  • Ester, M., Kriegel, H.-P., Sander, J., & Xu, X. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96).
  • Guha, S., Rastogi, R., & Shim, K. (1998). CURE: An efficient clustering algorithm for large databases. ACM SIGMOD Record, 27(2), 73-84.
  • Jarvis, R. & Patrick, E. (1973). Clustering using a similarity measure based on shared nearest neighbors. IEEE Transactions on Computers, 100(1), 104-125.
  • Karypis, G., Han, E. H., & Kumar, V. (1999). Chameleon: A hierarchical clustering algorithm using dynamic modeling. IEEE Computer Society.
  • Karypis, G. & Han, E. H. (2003). Design and analysis of clustering algorithms for massive datasets. Computational Geometry: Theory and Applications.
  • Khan, M. A. & Ahmad, A. (2004). Cluster center initialization methods for K-means clustering. Research Journal of Applied Sciences, 1(1), 121-125.
  • Tan, P. N., Steinbach, M., & Kumar, V. (2006). Introduction to Data Mining. Addison-Wesley.
  • Wang, H., Wang, J., & Chen, Z. (2015). A survey of clustering algorithms in data mining. International Journal of Advanced Computer Science and Applications, 6(1), 174-180.
  • Yuan, Z., Wang, S., & Li, K. (2008). A survey of clustering algorithms in data mining. International Conference on Data Mining.

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