Graph Clustering, also known as network clustering, is a technique for partitioning a graph into clusters or communities of nodes based on their structural properties[1]. Graph clustering is used in various applications such as social network analysis, image segmentation, bioinformatics, and more. The goal of graph clustering is to group the nodes in a way to maximizes the similarity within the group and minimizes the similarity between them[2]. These two similarities are usually measured using various metrics such as modularity, Normalized Mutual Information(NMI), Adjusted Rand Index(ARI) and FowlkesMallows Index(FMI).

We propose a novel clustering method that is an extension of ideas inher- ent to scale-space clustering and support-vector clustering. Like the lat- ter, it associates every data point with a vector in Hilbert space, and like the former it puts emphasis on their total sum, that is equal to the scale- space probability function. The novelty of our approach is the study of an operator in Hilbert space, represented by the Schr odinger equation of which the probability function is a solution. This Schr odinger equation contains a potential function that can be derived analytically from the probability function. The method has one variable parameter, the scale of its Gaussian kernel.

We propose a new assumption in outlier detection: Normal data instances are commonly located in the area that there is hardly any fluctuation on data density, while outliers are often appeared in the area that there is violent fluctuation on data density. And based on this hypothesis, we apply a novel density-based approach to unsupervised outlier detection. This approach, called Quantum Clustering (QC), deals with unlabeled data processing and constructs a potential function to find the centroids of clusters and the outliers. The experiments show that the potential function could clearly find the hidden outliers in data points effectively. Besides, by using QC, we could find more subtle outliers by adjusting the parameter $\sigma$. Moreover, our approach is also evaluated on two datasets (Air Quality Detection and Darwin Correspondence Project) from two different research areas, and the results show the wide applicability of our method.

Quantum Clustering is a powerful method to detect clusters in data with mixed density. However, it is very sensitive to a length parameter that is inherent to the Schr\"odinger equation. In addition, linking data points into clusters requires local estimates of covariance that are also controlled by length parameters. This raises the question of how to adjust the control parameters of the Schr\"odinger equation for optimal clustering. We propose a probabilistic framework that provides an objective function for the goodness-of-fit to the data, enabling the control parameters to be optimised within a Bayesian framework. This naturally yields probabilities of cluster membership and data partitions with specific numbers of clusters. The proposed framework is tested on real and synthetic data sets, assessing its validity by measuring concordance with known data structure by means of the Jaccard score (JS). This work also proposes an objective way to measure performance in unsupervised learning that correlates very well with JS.

The mixture of Gaussian distributions, a soft version of k-means , is considered a state-of-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color, texture, and shapes. In this algorithm, each class is described by a Gaussian distribution, defined by its mean and covariance. The data is described by a weighted sum of these Gaussian distributions. We propose a new method, inspired by quantum interference in physics. Instead of modeling each class distribution directly, we model a class wave function such that its magnitude square is the class Gaussian distribution. We then mix the class wave functions to create the mixture wave function. The final mixture distribution is then the magnitude square of the mixture wave function. As a result, we observe the quantum class interference phenomena, not present in the Gaussian mixture model. We show that the quantum method outperforms the Gaussian mixture method in every aspect of the estimations. It provides more accurate estimations of all distribution parameters, with much less fluctuations, and it is also more robust to data deformations from the Gaussian assumptions. We illustrate our method for color segmentation as an example application.

We propose a novel clustering method that is an extension of ideas inherent to scale-space clustering and support-vector clustering. Like the latter, it associates every data point with a vector in Hilbert space, and like the former it puts emphasis on their total sum, that is equal to the scalespace probability function. The novelty of our approach is the study of an operator in Hilbert space, represented by the Schrödinger equation of which the probability function is a solution. This Schrödinger equation contains a potential function that can be derived analytically from the probability function.

We propose a novel clustering method that is an extension of ideas inherent to scale-space clustering and support-vector clustering. Like the latter, it associates every data point with a vector in Hilbert space, and like the former it puts emphasis on their total sum, that is equal to the scalespace probability function. The novelty of our approach is the study of an operator in Hilbert space, represented by the Schrödinger equation of which the probability function is a solution. This Schrödinger equation contains a potential function that can be derived analytically from the probability function.

We propose a novel clustering method that is an extension of ideas inherent toscale-space clustering and support-vector clustering. Like the latter, itassociates every data point with a vector in Hilbert space, and like the former it puts emphasis on their total sum, that is equal to the scalespace probabilityfunction. The novelty of our approach is the study of an operator in Hilbert space, represented by the Schrödinger equation of which the probability function is a solution. This Schrödinger equation contains a potential function that can be derived analytically from the probability function.