Soft spectral clustering ensemble applied to image segmentation

The spectral clustering algorithm's space complexity is O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), while time complexity is O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ). When dealing with large amounts of data, the memory will overflow and run-time is too long. For the general problem of spectral clustering, if the clustering data of sub-problem between the original problem has the same probability distribution, it can be applied to divide and conquer strategy for the problem of spectral clustering, by the spectral clustering results of sub-problems to get the spectral clustering results of original problem. To spectral clustering image segmentation as a research object, we will discuss the divide and conquer strategy for spectral clustering in this paper. Experiments show that the application of divide and conquer method for spectral clustering image segmentation, we can get a perfect performance in image segmentation.

In the image segmentation, the spectral clustering algorithm are facing the problems, that the similarity matrix and Laplace matrix requires a lot of computing and storage, which limits its expansion in the large-scale image. Aiming at these problems, a semi-supervised spectrum clustering algorithm based on the Nystrom approximation was proposed. In the algorithm, adopting the Nystrom approximation method to estimate the similarity matrix, which effectively reduces the amount of computation and storage of the spectral clustering algorithm. Finally, on the Brodatz texture library, the image segmentation experiments showed the feasibility and effectiveness of the algorithm.

Recently, more and more multi-source data are widely used in many real world applications. This kind of data is high dimensional and comes from different resources, which are often the attribute information and similarity information of the same data. It is challenging to use these two types of information to deal with the high dimensional problem simultaneously. A natural way to adopt is a two-step procedure: it utilizes feature integration or kernel integration to combine these two types of information first and then perform dimensional reduction like principal component analysis or various manifold learning algorithms. Different from that, we proposed to deal with these problems in a unified framework which combines discriminative K-means clustering and spectral clustering together. Compared with those separate two-step procedure, information integration and dimension reduction can benefit from each other in our method to promote clustering performance.In addition, discriminative K-means clustering has incorporated K-means and linear discriminant analysis to promote clustering and tackle high dimensional problem. Spectral clustering can reduce the original dimension easily due to the singular value decomposition. Thus it is a good way to combine discriminative K-means and spectral clustering to improve clustering and deal with high dimensional problem. Experimental results on multiple real world data sets verified its effectiveness.

The problem of clustering is to partition the dataset into groups such that elements belonging to the same group are similar and elements belonging to the different groups are dissimilar. The unsupervised nature of the problem makes it widely applicable and also tough to solve objectively. Clustering in the context of image data is referred to as image segmentation. Distance based methods such as K-means fail to detect the non-globular clusters and hence spectral clustering was proposed to overcome this problem. This method detects the non globular structures by projecting the data set into a subspace, in which the usual clustering methods work well. Gamma convergence is the study of asymptotic behavior of minimizers of a family of minimization problems. Such a limit of minimizers is referred to as the gamma limit. Calculating the gamma limit for various variational problems has been proved useful - giving a different algorithm and insights into why existing methods work. In this article, we calculate the gamma limit of the spectral clustering methods, analyze its properties, and compare them with minimum spanning tree based clustering methods and spectral clustering methods.

Popular clustering algorithms, such as K-means (KM) and expectation maximization (EM), are sensitive to the initialization of cluster centers. In contrast, recently proposed K-harmonic means (KHM) algorithm is more robust to the randomness of the initialization. However, KHM works best when the dimensionality of the data (N) is small (usually less than 8). Because the dimensionality of features that are used for many clustering problems in image/video and speech processing is large, the benefits of KHM cannot be exploited. Based upon this observation, this paper proposes a novel method to employ KHM for high-dimensional data so as to realize initialization-independent clustering. The proposed method employs efficient spectral clustering techniques whereby the affinity matrix of the data is decomposed into its eigenvectors and k (total number of clusters) eigenvectors corresponding to the k largest eigenvalues are retained. That is, we represent N-D data by k-D transformed data when k < N and propose to employ KHM over this k-D transformed data. The assumption of k < N indeed encompasses a large number of significant video processing and computer vision problems where the use of KHM was not beneficial before. We demonstrate the effectiveness and the efficiency of the proposed algorithm for face clustering in the domains where the number of persons (k) is not large, such as anchorperson grouping, video-based speaker clustering in videoconferencing, and identity-based tracking in small office environments.

A robust adaptive clustering analysis method for automatic identification of clusters

Spectral clustering has become one of the most popular clustering methods due to its superior performance compared to the traditional clustering methods. However, the performance of spectral clustering would be limited by complex data, such as a huge number of samples and high dimensionality. To address this problem, some existing methods apply deep learning to learn the lower-dimensional representations, spectral clustering is then applied to the representations. Different from the existing methods that separate the two stages of feature representation learning and spectral clustering, in this paper, we propose Spectral Clustering Joint Deep Embedding (SCJDE), a method that simultaneously learns the feature representations and the spectral embedding of spectral clustering via a deep autoencoder. Moreover, a sparsity constraint is imposed to generate better spectral embedding for spectral clustering. Finally, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> -means is performed on the spectral embedding to obtain clustering result. The proposed method can learn a good spectral embedding for spectral clustering by deep learning to obtain better clustering results. The experimental results on both synthetic and real-world datasets demonstrate the effectiveness of the proposed method.

Brain tumour segmentation from MRI using superpixels based spectral clustering

Spectral graph clustering methods have been a hot topic in the field of image segmentation. However, because the computational demands are needed for Spectral graph clustering methods, it has been severely limited to apply them into large data sets, such as high resolution image. It would be too expensive or even impractical for spectral decomposition to provide the optimal approximation in dealing with large or high-dimensional datasets. A novel approach aiming at reducing the computational requirements is proposed in this paper. Our approach focuses on Nystrom method for the solution of eigen-function problems. This approach enables us to use a small number of samples to infer the overall clustering solution. Based on the proposed Nystrom sampling method, this paper presents a spectral clustering algorithm for massive data analysis, and the experiments show the method is both feasible and effective.

Spectral clustering has been shown to be more effective than most of the traditional clustering algorithms. However, the heavy computational cost of spectral clustering limits its applicability to large-scale clustering problems. To perform spectral clustering on large datasets, in this paper, we propose an accelerated spectral clustering method based on sparse presentation where each data point is presented as sparse linear combinations of a part of representative data points. The hubs that appear frequently in the nearest neighbor lists of other data points are selected as the representative data points, by which a proper spectral embedding is constructed. Taking advantage of the topological property of hubs, the proposed method is able to achieve scalable and accurate clustering results. We evaluated the proposed method on both synthetic and real-world datasets to show its effectiveness in comparison to the existing related methods.

While the Euclidean distance metric is commonly utilized in most soft subspace clustering algorithms, some robust distance metrics can also be considered for soft subspace clustering. In this study, a novel soft subspace clustering algorithm called Alternative Soft Subspace Clustering (ASSC) is proposed by incorporating the alternative distance metric into the framework of entropy weighting subspace clustering. The properties of ASSC are investigated and a theoretical analysis on robustness is established accordingly. Experiments on UCI data are conducted and the experimental results show the effectiveness of the proposed algorithm.

Computational scheme for comparison, color analysis and segmentation of images is proposed in this paper. First of all, two growing unsupervised learning algorithms are introduced. They create the so called compressed information model (CIM) of the image that replaces the original ldquoraw datardquo (the RGB pixels) with a smaller number of neurons. Then two main features are extracted from the CIM, namely the center-of-gravity of the model and the weighted average size. They could be used separately or in a two-dimensional fuzzy decision block for similarity analysis of pairs of images. Another type of image analysis is the image segmentation. A simple method for segmentation is described in the paper. It uses the unsupervised learning algorithms to generate small predetermined number of neurons (key-points of the image). Each key-point is considered as a center of the respective image segment and the area of pixels around this center corresponds to the color details of this segment. The proposed computational scheme and its application are demonstrated in the paper on test image examples.

A key goal of far-field activity analysis is to learn the usual pattern of activity in a scene and to detect statistically anomalous behavior. We propose a method for unsupervised, multi-attribute learning of a model of moving object tracks that enables fast reasoning about new tracks, both partial and complete. We group object tracks using spectral clustering and estimate the spectral embedding efficiently from a sample of tracks using the Nystrom approximation. Clusters are modeled as Gaussians in the embedding space and new tracks are projected into the embedding space and matched with the cluster models to detect anomalies. We show results on a week of data from a busy urban scene.

Spectral clustering has been successfully used in the field of pattern recognition and image processing. The efficiency of spectral clustering, however, depends heavily on the similarity measure adopted. A widely used similarity measure is the Gaussian kernel function where Euclidean distance is used. Unfortunately, the Gaussian kernel function is parameter sensitive and the Euclidean distance is usually not suitable to the complex distribution data. In this paper, a novel similarity measure called kernel fuzzy similarity measure is proposed first, Then this novel measure is integrated into spectral clustering to get a new clustering method: kernel fuzzy similarity based spectral clustering (KFSC). To alleviate the computational complexity of KFSC on image segmentation, Nystr\(\ddot{o}\)m method is used in KFSC. At last, the experiments on three synthetic texture images are made, and the results demonstrate the effectiveness of the proposed algorithm.

Simulated annealing spectral clustering algorithm for image segmentation