Multi-objective semi-supervised clustering for automatic pixel classification from remote sensing imagery

There are two notoriously hard problems in cluster analysis, estimating the number of clusters, and checking whether the population to be clustered is not actually homogeneous. Given a dataset, a clustering method and a cluster validation index, this paper proposes to set up null models that capture structural features of the data that cannot be interpreted as indicating clustering. Artificial datasets are sampled from the null model with parameters estimated from the original dataset. This can be used for testing the null hypothesis of a homogeneous population against a clustering alternative. It can also be used to calibrate the validation index for estimating the number of clusters, by taking into account the expected distribution of the index under the null model for any given number of clusters. The approach is illustrated by three examples, involving various different clustering techniques (partitioning around medoids, hierarchical methods, a Gaussian mixture model), validation indexes (average silhouette width, prediction strength and BIC), and issues such as mixed type data, temporal and spatial autocorrelation.

Transmissions in the mmWave spectrum benefit from a-priori knowledge of radio channel propagation models. This paper is concerned with one important task that helps provide a more accurate channel model, namely, the clustering of all multipath components arriving at the receiver. Our work focuses on directive transmissions in urban outdoor scenarios and shows the importance of the correct estimation of the number of clusters for mmWave radio channels simulated with a software ray-tracer tool. We investigate the effectiveness of k-means and k-power-means clustering algorithms in predicting the number of clusters through the use of cluster validity indices (CVIs) and score fusion techniques. Our investigation shows that clustering is a difficult task because the optimal number of clusters is not always given by one or by a combination of more CVIs. However, using score fusion methods, we find the optimal partitioning for the k-means algorithm based on the power and time of arrival of the multipath rays or based on their angle of arrival. When the k-power-means algorithm is used, the power of each arriving ray is the most important clustering factor, making the dominant received paths pull the other ones around them, to form a cluster. Thus, the number of clusters is smaller and the decision based on CVIs or score fusion factors easier to be taken.

Ground truth bias in external cluster validity indices

IMI2: A fuzzy clustering validity index for multiple imbalanced clusters

The Real time monitoring of forest area, coastal regions, sea, river basins, nation borders etc. helps in quick determination of devastations caused by natural or man-made catastrophes, which can lead to emergency situations. Real-time Segmentation of satellite images is essential to detect fire, floods, volcanoes, earthquakes etc. of a specific geographical zone. Effective determination of such calamities and taking proactive measures can save a lot of lives and natural resources. In this paper, an efficient FSM based architecture is proposed for performing segmentation of satellite Images procured from NASA’s Operational Land Imager (OLI) on Landsat 8 and Landsat 5. The K-means clustering algorithm even after five decades of it’s existence is quite effective and mostly used for big data applications, owing to its lower complexity. However, it’s effective implementation has started only in the last couple of years. Here a FSM-based reconfigurable architecture is proposed for K-means algorithm taking into consideration the real-time segmentation of satellite Images. Compared to other architectures in the literature, the proposed one has reduced hardware usage, lower area, power consumption with a satisfactory clock frequency, most importantly it is reconfigurable and can be used with the on-board circuitry within satellites. The testing is carried out on eight latest satellite images of natural and human devastations, taken from NASA’s OLI. The number of possible clusters within the geographical image is studied with the help of histogram analysis based on Otsu’s thresholding method. The performance analysis is carried out by computing the Peak Signal to Noise (PSNR) and Mean Structural Similarity Index (M-SSIM) of the resultant clusters. It is observed that by increasing the number of clusters, the detailed classes were effectively segmented and the quality of clustering is ensured by the improvement in PSNR and M-SSIM values. Comparison of the obtained clusters with their true land features also yielded satisfactory results.

In this paper, a new multi-objective (MO) fuzzy-clustering technique is developed for unsupervised land-cover classification in remote-sensing images. This technique automatically partitions the pixels in the spectral domain into several clusters. The new MO clustering algorithm uses the newly developed simulated-annealing-based multi-objective optimization technique (AMOSA) as the underlying optimization strategy. Centre-based cluster encoding is used. Each cluster is divided into several small hyperspherical sub-clusters, and the centres of all these small sub-clusters are encoded in a string to represent the whole cluster. For membership-value computation of points to different clusters, these sub-clusters are considered individually. However, for the purpose of objective-function evaluation, these sub-clusters are merged appropriately to form some variable number of whole clusters. Three objective functions, one reflecting the total compactness of the partitioning based on the Euclidean distance, one reflecting the total point-symmetrical compactness of the obtained partitioning and one reflecting the total line-symmetrical compactness of the obtained partitioning are considered here. These are optimized simultaneously using AMOSA in order to detect the appropriate number of clusters and the appropriate partitioning from remote-sensing image datasets. The point symmetry present in a particular partitioning is measured using a newly developed point-symmetry-based distance, whereas the line symmetry present in a particular partitioning is measured using a newly developed line-symmetry-based distance. Since AMOSA, as well as any other MO optimization technique, provides a set of Pareto-optimal solutions, a new method is also developed to determine a single solution from this set. Different land-cover regions in remote-sensing imagery have been classified using the proposed technique to establish its efficiency. Results are compared with those obtained by fuzzy C-means (FCM) clustering technique and a recently developed symmetry-based automatic clustering technique, the variable string length genetic point symmetry (VGAPS) technique, both qualitatively and quantitatively. Qualitative comparisons are also carried out with the segmentation results obtained by the mean-shift-based segmentation technique.

Purpose – The most commonly used approaches for cluster validation are based on indices but the majority of the existing cluster validity indices do not work well on data sets of different complexities. The purpose of this paper is to propose a new cluster validity index (ARSD index) that works well on all types of data sets. Design/methodology/approach – The authors introduce a new compactness measure that depicts the typical behaviour of a cluster where more points are located around the centre and lesser points towards the outer edge of the cluster. A novel penalty function is proposed for determining the distinctness measure of clusters. Random linear search-algorithm is employed to evaluate and compare the performance of the five commonly known validity indices and the proposed validity index. The values of the six indices are computed for all nc ranging from (nc min, nc max) to obtain the optimal number of clusters present in a data set. The data sets used in the experiments include shaped, Gaussian-like and real data sets. Findings – Through extensive experimental study, it is observed that the proposed validity index is found to be more consistent and reliable in indicating the correct number of clusters compared to other validity indices. This is experimentally demonstrated on 11 data sets where the proposed index has achieved better results. Originality/value – The originality of the research paper includes proposing a novel cluster validity index which is used to determine the optimal number of clusters present in data sets of different complexities.

Use of a fuzzy granulation–degranulation criterion for assessing cluster validity

DNA microarray technology is a fundamental tool in gene expression data analysis. The collection of datasets from the technology has underscored the need for quantitative analytical tools to examine such data. Due to the large number of genes and complex gene regulation networks, clustering is a useful exploratory technique for analyzing these data. Many clustering algorithms have been proposed to analyze microarray gene expression data, but very few of them evaluate the quality of the clusters. In this paper, a novel cluster analysis technique has been proposed without considering number of clusters a priori. The method computes a similarity measurement function based on which the clusters are merged and subsequently splits a cluster by computing the degree of separation of the cluster. The process of splitting and merging performs iteratively until the cluster validity index (i.e. DB index) degrades. The experimental result shows that the proposed cluster analysis technique gives comparable results on gene cancer dataset with existing methods. This study may help raise relevant issues in the extraction of meaningful biological information from microarray expression data. Keywords- DNA microarray data, Clustering technique, Cluster validity index, Similarity measurement, Splitting and Merging, Cancer data analysis

Abstract—This research presents an integrated framework for satellite image retrieval, segmentation, and visualization, utilizing Python-based algorithms and geospatial data processing methods. It incorporates Google Maps-based image acquisition, a Tkinter-powered interactive GUI, and the U-Net segmentation model to efficiently process satellite imagery. Satellite image segmentation, powered by U-Net, plays a vital role in geospatial analysis, enabling automated classification and extraction of key features from high-resolution imagery. The framework facilitates seamless high-resolution map generation, segmentation, and an- alytical visualization through interactive tools like bar graphs and pie charts. By leveraging U-Net’s robust architecture, this implementation enhances segmentation accuracy and supports applications in urban planning, environmental monitoring, and disaster management. Through the automation of retrieval, processing, and visualization of satellite imagery, this research advances geospatial intelligence and provides a scalable solution for efficient image segmentation workflows. Keywords—Satellite Image Segmentation, Land Cover Classi- fication, Remote Sensing, Image Processing, Semantic Segmen- tation, Deep Learning Models, Convolutional Neural Networks (CNNs), U-Net Architecture, Geospatial Analysis, Land Use Analysis

Semi-supervised clustering can be viewed as a clustering paradigm that exploits both labeled and unlabeled data to steer learning accurate data clusters and avoid local minimum solutions. Nonetheless, the attempts to refine existing semi-supervised clustering methods are relatively limited when compared to the advancements witnessed in the current benchmark methods in fully unsupervised clustering. This research introduces a novel semi-supervised method for deep clustering that leverages deep neural networks and fuzzy memberships to better capture the data partitions. In particular, the proposed Dual-Constraint-based Semi-Supervised Deep Clustering (DC-SSDEC) method utilizes two sets of pairwise soft constraints; "should-link" and "shouldNot-link", to guide the clustering process. The intended clustering task is expressed as an optimization of a newly designed objective function. Additionally, DC-SSDEC performance was evaluated through comprehensive experiments using three real-world and benchmark datasets. Moreover, a comparison with related state-of-the-art clustering techniques was conducted to showcase the DC-SSDEC outperformance. In particular, DC-SSDEC significance consists of the proposed dual-constraint formulation and its integration into a novel objective function. This contribution yielded an improvement in the resulting clustering performance compared to relevant state-of-the-art approaches. In addition, the assessment of the proposed model using real-world datasets represents another contribution of this research. In fact, increases of 3.25%, 1.44%, and 1.82% in the clustering accuracy were gained by DC-SSDEC over the best performing single-constraint-based approach, using MNIST, STL-10, and USPS datasets, respectively.

Identification of the correct number of clusters is an important consideration in clustering where several cluster validity indexes, primarily utilizing the Euclidean distance, have been used in the literature. The property of symmetry is observed in most clustering solutions. In this paper, the symmetry versions of nine cluster validity indexes, namely, Davies-Bouldin index, Dunn index, generalized Dunn index, point symmetry (PS) index, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> index, Xie-Beni index, FS index, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> index, and SV index, are proposed. It is empirically established that incorporation of the property of symmetry significantly improves the capabilities of these indexes in identifying the appropriate number of clusters. A recently developed PS-based genetic clustering technique, GAPS clustering, is used as the underlying partitioning algorithm. Results on six artificially generated and five real-life datasets show that symmetry-distance-based <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> index performs the best as compared to all the other eight indexes.

Determining the most proper number of cluster in fuzzy clustering by using artificial neural networks

Gene selection from microarray gene expression datasets and clustering of samples into different groups are important data mining tasks for disease identification. Selection of more interpretable genes from the gene expression dataset is an essential data-preprocessing task, which helps to study on cancer diseases. Gene selection during sample clustering is inherently a difficult task as there is no obvious criterion to guide the search. Simultaneous gene selection and sample clustering is a two-way data analysis technique which has recently gained attention in research area. The traditional clustering techniques are unable to handle noisy data properly. So, effective clustering algorithms are more desirable which can deal with the relevant and noise free data. Therefore, target genes selection before sample clustering is essential and of course effective if both the tasks are done simultaneously. In this chapter, optimal gene subset is selected and sample clustering is performed simultaneously using Multi-Objective Genetic Algorithm (MOGA). Different versions of MOGA are employed to choose the optimal gene subset, where natural number of optimal clusters of samples is automatically obtained at the end of the process. Non-dominated sorting genetic algorithm (NSGA), Strength pareto evolutionary algorithm (SPEA) and its modified version SPEA2 are applied for the purpose. The methods use nonlinear hybrid uniform cellular automata for generating initial population, tournament selection strategy, two-point crossover operation, and a suitable jumping gene mutation mechanism to maintain diversity in the population. It uses mutual correlation coefficient; internal and external cluster validation indices as objective functions to find out the non-dominated solutions. To measure the cluster validation indices, clustering algorithm is applied on data subset associated to chromosomes in the population to find out different clusters. After the convergence of genetic algorithm, the best solution from the non-dominated solutions is identified that provides the important genes and categorizes the samples into clusters. The experimental results express the correctness of the proposed simultaneous gene selection and sample categorization method. The goodness of optimality of the clusters obtained using different genetic algorithms is expressed by comparing various cluster validation indices.

DPCF: A framework for imputing missing values and clustering data in drug discovery process