The paper "Stop using the elbow criterion for k-means" argues against the common practice of using the elbow method to determine the optimal number of clusters (k) in k-means clustering. The authors demonstrate that the elbow method is unreliable, often identifying spurious elbows or missing genuine ones. They show this through theoretical analysis and empirical examples across various datasets and distance metrics, revealing how the within-cluster sum of squares (WCSS) curve, on which the elbow method relies, can behave unexpectedly. The paper advocates for abandoning the elbow method entirely in favor of more robust and theoretically grounded alternatives like the gap statistic, silhouette analysis, or information criteria, which offer statistically sound approaches to k selection.
This paper provides a comprehensive overview of percolation theory, focusing on its mathematical aspects. It explores bond and site percolation on lattices, examining key concepts like critical probability, the existence of infinite clusters, and critical exponents characterizing the behavior near the phase transition. The text delves into various methods used to study percolation, including duality, renormalization group techniques, and series expansions. It also discusses different percolation models beyond regular lattices, like continuum percolation and directed percolation, highlighting their unique features and applications. Finally, the paper connects percolation theory to other areas like random graphs, interacting particle systems, and the study of disordered media, showcasing its broad relevance in statistical physics and mathematics.
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Sort_Memories is a Python script that automatically sorts group photos based on the number of specified individuals present in each picture. Leveraging face detection and recognition, the script analyzes images, identifies faces, and groups photos based on the user-defined 'N' number of people desired in each output folder. This allows users to easily organize their photo collections by separating pictures of individuals, couples, small groups, or larger gatherings, automating a tedious manual process.
Hacker News commenters generally praised the project for its clever use of facial recognition to solve a common problem. Several users pointed out potential improvements, such as handling images where faces are partially obscured or not clearly visible, and suggested alternative approaches like clustering algorithms. Some discussed the privacy implications of using facial recognition technology, even locally. There was also interest in expanding the functionality to include features like identifying the best photo out of a burst or sorting based on other criteria like smiles or open eyes. Overall, the reception was positive, with commenters recognizing the project's practical value and potential.
Summary of Comments ( 13 )
https://news.ycombinator.com/item?id=43450550
HN users discuss the problems with the elbow method for determining the optimal number of clusters in k-means, agreeing it's often unreliable and subjective. Several commenters suggest superior alternatives, such as the silhouette coefficient, gap statistic, and information criteria like AIC/BIC. Some highlight the importance of considering the practical context and the "business need" when choosing the number of clusters, rather than relying solely on statistical methods. Others point out that k-means itself may not be the best clustering algorithm for all datasets, recommending DBSCAN and hierarchical clustering as potentially better suited for certain situations, particularly those with non-spherical clusters. A few users mention the difficulty in visualizing high-dimensional data and interpreting the results of these metrics, emphasizing the iterative nature of cluster analysis.
The Hacker News post titled "Stop using the elbow criterion for k-means" (https://news.ycombinator.com/item?id=43450550) discusses the linked arXiv paper which argues against using the elbow method for determining the optimal number of clusters in k-means clustering. The comments section is relatively active, featuring a variety of perspectives on the topic.
Several commenters agree with the premise of the article. They point out that the elbow method is often subjective and unreliable, leading to arbitrary choices for the number of clusters. Some users share anecdotal experiences of the elbow method failing to produce meaningful results or being difficult to interpret. One commenter suggests the gap statistic as a more robust alternative.
A recurring theme in the comments is the inherent difficulty of choosing the "right" number of clusters, especially in high-dimensional spaces. Some users argue that the optimal number of clusters is often dependent on the specific application and downstream analysis, rather than being an intrinsic property of the data. They suggest that domain knowledge and interpretability should play a significant role in the decision-making process.
One commenter points out that the elbow method is particularly problematic when the clusters are not well-separated or when the data has a complex underlying structure. They suggest using visualization techniques, like dimensionality reduction, to gain a better understanding of the data before attempting to cluster it.
Another comment thread discusses the limitations of k-means clustering itself, regardless of the method used to choose k. Users highlight the algorithm's sensitivity to initial conditions and its assumption of spherical clusters. They propose alternative clustering methods, such as DBSCAN and hierarchical clustering, which may be more suitable for certain types of data.
A few commenters defend the elbow method, arguing that it can be a useful starting point for exploratory data analysis. They acknowledge its limitations but suggest that it can provide a rough estimate of the number of clusters, which can be refined using other techniques.
Finally, some commenters discuss the practical implications of choosing the wrong number of clusters. They highlight the potential for misleading results and incorrect conclusions, emphasizing the importance of careful consideration and validation. One commenter suggests using metrics like silhouette score or Calinski-Harabasz index to assess the quality of the clustering.
Overall, the comments section reflects a general consensus that the elbow method is not a reliable technique for determining the optimal number of clusters in k-means. Commenters offer various alternative approaches, emphasize the importance of domain knowledge and data visualization, and discuss the broader challenges of clustering high-dimensional data.