Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level structure. This is often overlooked in the design and analysis of graph clustering algorithms which make strong simplifying assumptions about the structure of the graph. This thesis addresses the natural question of whether the structure of clusters can be learned efficiently and describes four new algorithmic results for learning such structure in graphs and hypergraphs. All of the presented theoretical results are extensively evaluated on both synthetic and real-word datasets of different domains, including image classification and segmentation, migration networks, co-authorship networks, and natural language processing. These experimental results demonstrate that the newly developed algorithms are practical, effective, and immediately applicable for learning the structure of clusters in real-world data.

Recently the deep learning has shown its advantage in representation learning and clustering for time series data. Despite the considerable progress, the existing deep time series clustering approaches mostly seek to train the deep neural network by some instance reconstruction based or cluster distribution based objective, which, however, lack the ability to exploit the sample-wise (or augmentation-wise) contrastive information or even the higher-level (e.g., cluster-level) contrastiveness for learning discriminative and clustering-friendly representations. In light of this, this paper presents a deep temporal contrastive clustering (DTCC) approach, which for the first time, to our knowledge, incorporates the contrastive learning paradigm into the deep time series clustering research. Specifically, with two parallel views generated from the original time series and their augmentations, we utilize two identical auto-encoders to learn the corresponding representations, and in the meantime perform the cluster distribution learning by incorporating a k-means objective. Further, two levels of contrastive learning are simultaneously enforced to capture the instance-level and cluster-level contrastive information, respectively. With the reconstruction loss of the auto-encoder, the cluster distribution loss, and the two levels of contrastive losses jointly optimized, the network architecture is trained in a self-supervised manner and the clustering result can thereby be obtained. Experiments on a variety of time series datasets demonstrate the superiority of our DTCC approach over the state-of-the-art.

We study the problem of graph clustering under a broad class of objectives in which the quality of a cluster is defined based on the ratio between the number of edges in the cluster, and the total weight of vertices in the cluster. We show that our definition is closely related to popular clustering measures, namely normalized associations, which is a dual of the normalized cut objective, and normalized modularity. We give a linear time constant-approximate algorithm for our objective, which implies the first constant-factor approximation algorithms for normalized modularity and normalized associations.

Training of a Machine Learning model requires sufficient data. The sufficiency of the data is not always about the quantity, but about the relevancy and reduced redundancy. Data-generating processes create massive amounts of data. When used raw, such big data is causing much computational resource utilization. Instead of using the raw data, a proper Condensed Representation can be used instead. Combining K-means, a well-known clustering method, with some correction and refinement facilities a novel Condensed Representation method for Machine Learning applications is introduced. To present the novel method meaningfully and visually, synthetically generated data is employed. It has been shown that by using the condensed representation, instead of the raw data, acceptably accurate model training is possible.

Consensus clustering aggregates partitions in order to find a better fit by reconciling clustering results from different sources/executions. In practice, there exist noise and outliers in clustering task, which, however, may significantly degrade the performance. To address this issue, we propose a novel algorithm -- robust consensus clustering that can find common ground truth among experts' opinions, which tends to be minimally affected by the bias caused by the outliers. In particular, we formalize the robust consensus clustering problem as a constraint optimization problem, and then derive an effective algorithm upon alternating direction method of multipliers (ADMM) with rigorous convergence guarantee. Our method outperforms the baselines on benchmarks. We apply the proposed method to the real-world advertising campaign segmentation and forecasting tasks using the proposed consensus clustering results based on the similarity computed via Kolmogorov-Smirnov Statistics. The accurate clustering result is helpful for building the advertiser profiles so as to perform the forecasting.

The combination of conduct, emotion, motivation, and thinking is referred to as personality. To shortlist candidates more effectively, many organizations rely on personality predictions. The firm can hire or pick the best candidate for the desired job description by grouping applicants based on the necessary personality preferences. A model is created to identify applicants' personality types so that employers may find qualified candidates by examining a person's facial expression, speech intonation, and resume. Additionally, the paper emphasises detecting the changes in employee behaviour. Employee attitudes and behaviour towards each set of questions are being examined and analysed. Here, the K-Modes clustering method is used to predict employee well-being, including job pressure, the working environment, and relationships with peers, utilizing the OCEAN Model and the CNN algorithm in the AVI-AI administrative system. Findings imply that AVIs can be used for efficient candidate screening with an AI decision agent. The study of the specific field is beyond the current explorations and needed to be expanded with deeper models and new configurations that can patch extremely complex operations.

In recent years, reinforcement learning (RL) has become increasingly successful in its application to science and the process of scientific discovery in general. However, while RL algorithms learn to solve increasingly complex problems, interpreting the solutions they provide becomes ever more challenging. In this work, we gain insights into an RL agent's learned behavior through a post-hoc analysis based on sequence mining and clustering. Specifically, frequent and compact subroutines, used by the agent to solve a given task, are distilled as gadgets and then grouped by various metrics. This process of gadget discovery develops in three stages: First, we use an RL agent to generate data, then, we employ a mining algorithm to extract gadgets and finally, the obtained gadgets are grouped by a density-based clustering algorithm. We demonstrate our method by applying it to two quantum-inspired RL environments. First, we consider simulated quantum optics experiments for the design of high-dimensional multipartite entangled states where the algorithm finds gadgets that correspond to modern interferometer setups. Second, we consider a circuit-based quantum computing environment where the algorithm discovers various gadgets for quantum information processing, such as quantum teleportation. This approach for analyzing the policy of a learned agent is agent and environment agnostic and can yield interesting insights into any agent's policy.

A major challenge when using k-means clustering often is how to choose the parameter k, the number of clusters. In this letter, we want to point out that it is very easy to draw poor conclusions from a common heuristic, the "elbow method". Better alternatives have been known in literature for a long time, and we want to draw attention to some of these easy to use options, that often perform better. This letter is a call to stop using the elbow method altogether, because it severely lacks theoretic support, and we want to encourage educators to discuss the problems of the method -- if introducing it in class at all -- and teach alternatives instead, while researchers and reviewers should reject conclusions drawn from the elbow method.

There has been an immense progress in the field of machine learning in the last years. In particular, deep learning has led to the development of very complex models which yield highly accurate results but lack explainability and interpretability. To overcome this defect, the field of Explainable Artificial Intelligence (XAI for short, see for example [1-3]) has recently significantly increased momentum.

Among many clustering algorithms, the K-means clustering algorithm is widely used because of its simple algorithm and fast convergence. However, this algorithm suffers from incomplete data, where some samples have missed some of their attributes. To solve this problem, we mainly apply MM principles to restore the symmetry of the data, so that K-means could work well. We give the pseudo-code of the algorithm and use the standard datasets for experimental verification. Clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters). It is the main task of exploratory data mining, and a common technique for statistical data analysis used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, and bioinformatics [1]-[3].