This paper presents a unified view of segmentation algorithms based on eigenvectors of the affinity matrix. These methods are attractive due to their simplicity and stability. The paper shows that while these algorithms appear different, they are closely related and all use dominant eigenvectors for segmentation. The paper proves results on eigendecompositions of block matrices to analyze the performance of these algorithms and motivates a new hybrid algorithm. It also discusses the application of these algorithms to affinity matrices derived from images. The paper reviews four algorithms: Perona and Freeman (PF), Shi and Malik (SM), Scott and Longuet-Higgins (SLH), and Costeira and Kanade (CK). The PF algorithm uses the first eigenvector of the affinity matrix to segment points. The SM algorithm uses the second generalized eigenvector of the affinity matrix. The SLH algorithm constructs a matrix Q from the first k eigenvectors of the affinity matrix and uses it for segmentation. The CK algorithm uses singular values of the measurement matrix to segment points into rigidly moving bodies. The paper analyzes these algorithms in simple grouping settings. It shows that when the affinity matrix has constant blocks, all three algorithms (PF, SM, SLH) work well. The SLH algorithm is particularly effective in extracting discrete segmentation. When the blocks are not constant, normalization of the affinity matrix is important for accurate segmentation. The paper also discusses the application of these algorithms to images. It shows that eigenvectors of the affinity matrix can be used to segment images, but the information is not always clear. The SLH algorithm, when applied to the normalized affinity matrix, provides a clear segmentation. The paper also shows that the CK algorithm is nearly identical to the SLH algorithm with a particular definition of affinity. The paper concludes that these algorithms are effective for segmentation, and their unified view provides a foundation for future research. The paper also highlights the importance of normalization and the use of the first k eigenvectors for accurate segmentation.This paper presents a unified view of segmentation algorithms based on eigenvectors of the affinity matrix. These methods are attractive due to their simplicity and stability. The paper shows that while these algorithms appear different, they are closely related and all use dominant eigenvectors for segmentation. The paper proves results on eigendecompositions of block matrices to analyze the performance of these algorithms and motivates a new hybrid algorithm. It also discusses the application of these algorithms to affinity matrices derived from images. The paper reviews four algorithms: Perona and Freeman (PF), Shi and Malik (SM), Scott and Longuet-Higgins (SLH), and Costeira and Kanade (CK). The PF algorithm uses the first eigenvector of the affinity matrix to segment points. The SM algorithm uses the second generalized eigenvector of the affinity matrix. The SLH algorithm constructs a matrix Q from the first k eigenvectors of the affinity matrix and uses it for segmentation. The CK algorithm uses singular values of the measurement matrix to segment points into rigidly moving bodies. The paper analyzes these algorithms in simple grouping settings. It shows that when the affinity matrix has constant blocks, all three algorithms (PF, SM, SLH) work well. The SLH algorithm is particularly effective in extracting discrete segmentation. When the blocks are not constant, normalization of the affinity matrix is important for accurate segmentation. The paper also discusses the application of these algorithms to images. It shows that eigenvectors of the affinity matrix can be used to segment images, but the information is not always clear. The SLH algorithm, when applied to the normalized affinity matrix, provides a clear segmentation. The paper also shows that the CK algorithm is nearly identical to the SLH algorithm with a particular definition of affinity. The paper concludes that these algorithms are effective for segmentation, and their unified view provides a foundation for future research. The paper also highlights the importance of normalization and the use of the first k eigenvectors for accurate segmentation.