Linear Clustering Method Research Articles

Detection of Massive Oil Spills in Sun Glint Optical Imagery through Super-Pixel Segmentation

Large volumes of crude oil accidentally released into the sea may cause irreversible adverse impacts on marine and coastal environments. Large swath optical imagery, acquired using platforms such as the moderate-resolution imaging spectroradiometer (MODIS), is frequently used for massive oil spill detection, attributing to its large coverage and short global revisit, providing rich data for oil spill monitoring. The aim of this study was to develop a suitable approach for massive oil spill detection in sun glint optical imagery. Specifically, preprocessing procedures were conducted to mitigate the inhomogeneous light field over the spilled area caused by sun glint, enhance the target boundary contrast, and maintain the internal homogeneity within the target. The image was then segmented into super-pixels based on a simple linear clustering method with similar characteristics of color, brightness, and texture. The neighborhood super-pixels were merged into target objects through the region adjacency graph method based on the Euclidean distance of their colors with an adaptive termination threshold. Oil slicks from the generated bright/dark objects were discriminated through a decision tree with parameters based on spectral and spatial characteristics. The proposed approach was applied to oil spill detection in MODIS images acquired during the Montara oil spill in 2009, with an overall extraction precision of 0.8, recall of 0.838, and F1-score of 0.818. Such an approach is expected to provide timely and accurate oil spill detection for disaster emergency response and ecological impact assessment.

Silhouette Analysis for Performance Evaluation in Machine Learning with Applications to Clustering.

Grouping the objects based on their similarities is an important common task in machine learning applications. Many clustering methods have been developed, among them k-means based clustering methods have been broadly used and several extensions have been developed to improve the original k-means clustering method such as k-means ++ and kernel k-means. K-means is a linear clustering method; that is, it divides the objects into linearly separable groups, while kernel k-means is a non-linear technique. Kernel k-means projects the elements to a higher dimensional feature space using a kernel function, and then groups them. Different kernel functions may not perform similarly in clustering of a data set and, in turn, choosing the right kernel for an application could be challenging. In our previous work, we introduced a weighted majority voting method for clustering based on normalized mutual information (NMI). NMI is a supervised method where the true labels for a training set are required to calculate NMI. In this study, we extend our previous work of aggregating the clustering results to develop an unsupervised weighting function where a training set is not available. The proposed weighting function here is based on Silhouette index, as an unsupervised criterion. As a result, a training set is not required to calculate Silhouette index. This makes our new method more sensible in terms of clustering concept.

Weighted Mutual Information for Aggregated Kernel Clustering.

Background: A common task in machine learning is clustering data into different groups based on similarities. Clustering methods can be divided in two groups: linear and nonlinear. A commonly used linear clustering method is K-means. Its extension, kernel K-means, is a non-linear technique that utilizes a kernel function to project the data to a higher dimensional space. The projected data will then be clustered in different groups. Different kernels do not perform similarly when they are applied to different datasets. Methods: A kernel function might be relevant for one application but perform poorly to project data for another application. In turn choosing the right kernel for an arbitrary dataset is a challenging task. To address this challenge, a potential approach is aggregating the clustering results to obtain an impartial clustering result regardless of the selected kernel function. To this end, the main challenge is how to aggregate the clustering results. A potential solution is to combine the clustering results using a weight function. In this work, we introduce Weighted Mutual Information (WMI) for calculating the weights for different clustering methods based on their performance to combine the results. The performance of each method is evaluated using a training set with known labels. Results: We applied the proposed Weighted Mutual Information to four data sets that cannot be linearly separated. We also tested the method in different noise conditions. Conclusions: Our results show that the proposed Weighted Mutual Information method is impartial, does not rely on a single kernel, and performs better than each individual kernel specially in high noise.

Euler Clustering on Large-Scale Dataset

Our concern is nonlinear clustering on large-scale dataset. While existing popular kernels (RBF, Polynomials, Spatial Pyramid, etc.) are popularly used for implicitly mapping data into a high-dimensional or infinite dimensional space in order to generalise linear clustering methods, using these kernels cannot make kernel clustering approaches directly applicable for large scale dataset, since large scale kernel matrix or similarity matrix consumes a lot of memory (e.g., 7,450 GB memory over 1 million samples of data). To solve this problem, we introduce an Euler clustering approach. Euler clustering employs Euler kernels in order to intrinsically map the input data onto a complex space of the same dimension as the input or twice, so that Euler clustering can get rid of kernel trick and does not need to rely on any approximation or random sampling on kernel function/matrix, whilst performing a more robust nonlinear clustering against noise and outliers. Moreover, since the original Euler kernel cannot generate a non-negative similarity matrix and thus is inapplicable to spectral clustering, we introduce a positive Euler kernel, and more importantly we have proved when it can generate a non-negative similarity matrix. We apply Euler kernel and the proposed positive Euler kernel to kernel k-means and spectral clustering so as to develop Euler k-means and Euler spectral clustering, respectively. An efficient Stiefel-manifold-based gradient method and an equivalent weighted positive Euler k-means are derived for fast computation of Euler spectral clustering and further alleviating the impact of discretization of the cluster membership indicators in Euler spectral clustering. The results show that the proposed Euler clustering approach achieves overall better clustering performance compared to using popular Mercer kernels and approximation models, whilst keeping the computational complexity of the same magnitude as the most popular linear clustering method k-means.

COMPARISON OF TWO SIMPLIFICATION METHODS FOR SHORELINE EXTRACTION FROM DIGITAL ORTHOPHOTO IMAGES

Abstract. The coastal ecosystems are very sensitive to external influences. Coastal resources such as sand dunes, coral reefs and mangroves has vital importance to prevent coastal erosion. Human based effects also threats the coastal areas. Therefore, the change of coastal areas should be monitored. Up-to-date, accurate shoreline information is indispensable for coastal managers and decision makers. Remote sensing and image processing techniques give a big opportunity to obtain reliable shoreline information. In the presented study, NIR bands of seven 1:5000 scaled digital orthophoto images of Riga Bay-Latvia have been used. The Object-oriented Simple Linear Clustering method has been utilized to extract shoreline of Riga Bay. Bend and Douglas-Peucker methods have been used to simplify the extracted shoreline to test the effect of both methods. Photogrammetrically digitized shoreline has been taken as reference data to compare obtained results. The accuracy assessment has been realised by Digital Shoreline Analysis tool. As a result, the achieved shoreline by the Bend method has been found closer to the extracted shoreline with Simple Linear Clustering method.

Graph PCA Hashing for Similarity Search

This paper proposes a new hashing framework to conduct similarity search via the following steps: first, employing linear clustering methods to obtain a set of representative data points and a set of landmarks of the big dataset; second, using the landmarks to generate a probability representation for each data point. The proposed probability representation method is further proved to preserve the neighborhood of each data point. Third, PCA is integrated with manifold learning to lean the hash functions using the probability representations of all representative data points. As a consequence, the proposed hashing method achieves efficient similarity search (with linear time complexity) and effective hashing performance and high generalization ability (simultaneously preserving two kinds of complementary similarity structures, i.e., local structures via manifold learning and global structures via PCA). Experimental results on four public datasets clearly demonstrate the advantages of our proposed method in terms of similarity search, compared to the state-of-the-art hashing methods.

Hierarchical and Non-Hierarchical Linear and Non-Linear Clustering Methods to Shakespeare Authorship Questionn

A few literary scholars have long claimed that Shakespeare did not write some of his best plays (history plays and tragedies) and proposed at one time or another various suspect authorship candidates. Most modern-day scholars of Shakespeare have rejected this claim, arguing that strong evidence that Shakespeare wrote the plays and poems being his name appears on them as the author. This has caused and led to an ongoing scholarly academic debate for quite some long time. Stylometry is a fast-growing field often used to attribute authorship to anonymous or disputed texts. Stylometric attempts to resolve this literary puzzle have raised interesting questions over the past few years. The following paper contributes to “the Shakespeare authorship question” by using a mathematically-based methodology to examine the hypothesis that Shakespeare wrote all the disputed plays traditionally attributed to him. More specifically, the mathematically based methodology used here is based on Mean Proximity, as a linear hierarchical clustering method, and on Principal Components Analysis, as a non-hierarchical linear clustering method. It is also based, for the first time in the domain, on Self-Organizing Map U-Matrix and Voronoi Map, as non-linear clustering methods to cover the possibility that our data contains significant non-linearities. Vector Space Model (VSM) is used to convert texts into vectors in a high dimensional space. The aim of which is to compare the degrees of similarity within and between limited samples of text (the disputed plays). The various works and plays assumed to have been written by Shakespeare and possible authors notably, Sir Francis Bacon, Christopher Marlowe, John Fletcher, and Thomas Kyd, where “similarity” is defined in terms of correlation/distance coefficient measure based on the frequency of usage profiles of function words, word bi-grams, and character triple-grams. The claim that Shakespeare authored all the disputed plays traditionally attributed to him is falsified in favor of the alternative authors according to the stylistic criteria and analytic methodology used. The result of this validated analysis is empirically-based, objective, and involves replicable evidence which can be used in conjunction with existing arguments to resolve the question of whether or not Shakespeare of Stratford-upon-Avon wrote all the disputed plays traditionally attributed to him.

Long-term system load forecasting based on data-driven linear clustering method

In this paper, a data-driven linear clustering (DLC) method is proposed to solve the long-term system load forecasting problem caused by load fluctuation in some developed cities. A large substation load dataset with annual interval is utilized and firstly preprocessed by the proposed linear clustering method to prepare for modelling. Then optimal autoregressive integrated moving average (ARIMA) models are constructed for the sum series of each obtained cluster to forecast their respective future load. Finally, the system load forecasting result is obtained by summing up all the ARIMA forecasts. From error analysis and application results, it is both theoretically and practically proved that the proposed DLC method can reduce random forecasting errors while guaranteeing modelling accuracy, so that a more stable and precise system load forecasting result can be obtained.

Optimized Thermal Compensation Method Using Clustering and Drifted Response Stability for Total Power Radiometer Calibration

Radiometer calibration using a compensation method based on temperature drift under a variety of environmental conditions can be used for airborne applications because of limitations on weight and power. Accordingly, the observation of the variation of the system states via analysis of the obtained response with temperature data is necessary to compensate the fluctuation of physical temperature for accurate calibration of the radiometer. However, the accuracy of the previous method (which uses one or more temperature probe) can rarely obtain an accurate estimated result; its accuracy is insufficient for high-precision measurement applications. Additionally, previous methods may cause unpredictable estimation errors when using regression methods with fewer measurable sensors. Therefore, more advanced compensation methods, which can compensate for the drift in radiometer output using temperature sensors (based on the analysis of the distinctive features of the temperature), are required to estimate the brightness temperature. In this paper, an optimized thermal compensation method using a selection of the optimal point for gain and offset probing to control the coefficients is analyzed using both the correlation-matrix-based hierarchical clustering and a comparison with the response stability for the training period. Then, the clustered temperature sensors of the radiometer system are used in the predictor variable to achieve optimum compensation of radiometer response variation. Next, the regression model of the multiple linear clustering method is compared the estimation accuracy for the selected training period and temperature sensors. Improved results relative to the reference method are achieved using the proposed model in experiments.

Hierarchical and Non-Hierarchical Linear and Non-Linear Clustering Methods to “Shakespeare Authorship Question”

A few literary scholars have long claimed that Shakespeare did not write some of his best plays (history plays and tragedies) and proposed at one time or another various suspect authorship candidates. Most modern-day scholars of Shakespeare have rejected this claim, arguing that strong evidence that Shakespeare wrote the plays and poems being his name appears on them as the author. This has caused and led to an ongoing scholarly academic debate for quite some long time. Stylometry is a fast-growing field often used to attribute authorship to anonymous or disputed texts. Stylometric attempts to resolve this literary puzzle have raised interesting questions over the past few years. The following paper contributes to “the Shakespeare authorship question” by using a mathematically-based methodology to examine the hypothesis that Shakespeare wrote all the disputed plays traditionally attributed to him. More specifically, the mathematically based methodology used here is based on Mean Proximity, as a linear hierarchical clustering method, and on Principal Components Analysis, as a non-hierarchical linear clustering method. It is also based, for the first time in the domain, on Self-Organizing Map U-Matrix and Voronoi Map, as non-linear clustering methods to cover the possibility that our data contains significant non-linearities. Vector Space Model (VSM) is used to convert texts into vectors in a high dimensional space. The aim of which is to compare the degrees of similarity within and between limited samples of text (the disputed plays). The various works and plays assumed to have been written by Shakespeare and possible authors notably, Sir Francis Bacon, Christopher Marlowe, John Fletcher, and Thomas Kyd, where “similarity” is defined in terms of correlation/distance coefficient measure based on the frequency of usage profiles of function words, word bi-grams, and character triple-grams. The claim that Shakespeare authored all the disputed plays traditionally attributed to him is falsified in favor of the alternative authors according to the stylistic criteria and analytic methodology used. The result of this validated analysis is empirically-based, objective, and involves replicable evidence which can be used in conjunction with existing arguments to resolve the question of whether or not Shakespeare of Stratford-upon-Avon wrote all the disputed plays traditionally attributed to him.