Cluster analysis requires many decisions: the clustering method and the implied reference model, the number of clusters and, often, several hyper-parameters and algorithms' tunings. In practice, one produces several partitions, and a final one is chosen based on validation or selection criteria. There exist an abundance of validation methods that, implicitly or explicitly, assume a certain clustering notion. Moreover, they are often restricted to operate on partitions obtained from a specific method. In this paper, we focus on groups that can be well separated by quadratic or linear boundaries. The reference cluster concept is defined through the quadratic discriminant score function and parameters describing clusters' size, center and scatter. We develop two cluster-quality criteria called quadratic scores. We show that these criteria are consistent with groups generated from a general class of elliptically-symmetric distributions. The quest for this type of groups is common in applications. The connection with likelihood theory for mixture models and model-based clustering is investigated. Based on bootstrap resampling of the quadratic scores, we propose a selection rule that allows choosing among many clustering solutions. The proposed method has the distinctive advantage that it can compare partitions that cannot be compared with other state-of-the-art methods. Extensive numerical experiments and the analysis of real data show that, even if some competing methods turn out to be superior in some setups, the proposed methodology achieves a better overall performance.

Imbalanced learning is important and challenging since the problem of the classification of imbalanced datasets is prevalent in machine learning and data mining fields. Sampling approaches are proposed to address this issue, and cluster-based oversampling methods have shown great potential as they aim to simultaneously tackle between-class and within-class imbalance issues. However, all existing clustering methods are based on a one-time approach. Due to the lack of a priori knowledge, improper setting of the number of clusters often exists, which leads to poor clustering performance. Besides, the existing methods are likely to generate noisy instances. To solve these problems, this paper proposes a deep instance envelope network-based imbalanced learning algorithm with the multilayer fuzzy c-means (MlFCM) and a minimum interlayer discrepancy mechanism based on the maximum mean discrepancy (MIDMD). This algorithm can guarantee high quality balanced instances using a deep instance envelope network in the absence of prior knowledge. In the experimental section, thirty-three popular public datasets are used for verification, and over ten representative algorithms are used for comparison. The experimental results show that the proposed approach significantly outperforms other popular methods.

We selected 48 European cities and gathered their public transport timetables in the GTFS format. We utilized Uber's H3 spatial index to divide each city into hexagonal micro-regions. Based on the timetables data we created certain features describing the quantity and variety of public transport availability in each region. Next, we trained an auto-associative deep neural network to embed each of the regions. Having such prepared representations, we then used a hierarchical clustering approach to identify similar regions. To do so, we utilized an agglomerative clustering algorithm with a euclidean distance between regions and Ward's method to minimize in-cluster variance. Finally, we analyzed the obtained clusters at different levels to identify some number of clusters that qualitatively describe public transport availability. We showed that our typology matches the characteristics of analyzed cities and allows succesful searching for areas with similar public transport schedule characteristics.

Representation learning of spatial and geographic data is a rapidly developing field which allows for similarity detection between areas and high-quality inference using deep neural networks. Past approaches however concentrated on embedding raster imagery (maps, street or satellite photos), mobility data or road networks. In this paper we propose the first approach to learning vector representations of OpenStreetMap regions with respect to urban functions and land-use in a micro-region grid. We identify a subset of OSM tags related to major characteristics of land-use, building and urban region functions, types of water, green or other natural areas. Through manual verification of tagging quality, we selected 36 cities were for training region representations. Uber's H3 index was used to divide the cities into hexagons, and OSM tags were aggregated for each hexagon. We propose the hex2vec method based on the Skip-gram model with negative sampling. The resulting vector representations showcase semantic structures of the map characteristics, similar to ones found in vector-based language models. We also present insights from region similarity detection in six Polish cities and propose a region typology obtained through agglomerative clustering.

Delirium is a common acute onset brain dysfunction in the emergency setting and is associated with higher mortality. It is difficult to detect and monitor since its presentations and risk factors can be different depending on the underlying medical condition of patients. In our study, we aimed to identify subtypes within the delirium population and build subgroup-specific predictive models to detect delirium using Medical Information Mart for Intensive Care IV (MIMIC-IV) data. We showed that clusters exist within the delirium population. Differences in feature importance were also observed for subgroup-specific predictive models. Our work could recalibrate existing delirium prediction models for each delirium subgroup and improve the precision of delirium detection and monitoring for ICU or emergency department patients who had highly heterogeneous medical conditions.

To process the learning data, the K-means algorithm in data mining starts with the first group of randomly selected centroids, which are used as the beginning points for every cluster, and then performs iterative (repetitive) calculations to optimize the positions of the centroids. You'll define a target number k, which refers to the number of centroids you need in the dataset. A centroid is the imaginary or real location representing the center of the cluster. Every data point is allocated to each of the clusters by reducing the in-cluster sum of squares. The K-means algorithm identifies k number of centroids, and then allocates every data point to the nearest cluster while keeping the centroids as small as possible.

We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors facilitating real-time measurement and rapid drop in storage costs. In particular, we consider the setting where the time series data on $N$ entities is generated from a Gaussian mixture model with autocorrelations over $k$ clusters in $\mathbb{R}^d$. Our main contribution is an algorithm to construct coresets for the maximum likelihood objective for this mixture model. Our algorithm is efficient, and under a mild boundedness assumption on the covariance matrices of the underlying Gaussians, the size of the coreset is independent of the number of entities $N$ and the number of observations for each entity, and depends only polynomially on $k$, $d$ and $1/\varepsilon$, where $\varepsilon$ is the error parameter. We empirically assess the performance of our coreset with synthetic data.

Gathering training data is a key step of any supervised learning task, and it is both critical and expensive. Critical, because the quantity and quality of the training data has a high impact on the performance of the learned function. Expensive, because most practical cases rely on humans-in-the-loop to label the data. The process of determining the correct labels is much more expensive than comparing two items to see whether they belong to the same class. Thus motivated, we propose a setting for training data gathering where the human experts perform the comparatively cheap task of answering pairwise queries, and the computer groups the items into classes (which can be labeled cheaply at the very end of the process). Given the items, we consider two random models for the classes: one where the set partition they form is drawn uniformly, the other one where each item chooses its class independently following a fixed distribution. In the first model, we characterize the algorithms that minimize the average number of queries required to cluster the items and analyze their complexity. In the second model, we analyze a specific algorithm family, propose as a conjecture that they reach the minimum average number of queries and compare their performance to a random approach. We also propose solutions to handle errors or inconsistencies in the experts' answers.

The quality of sleep has a deep impact on people's physical and mental health. People with insufficient sleep are more likely to report physical and mental distress, activity limitation, anxiety, and pain. Moreover, in the past few years, there has been an explosion of applications and devices for activity monitoring and health tracking. Signals collected from these wearable devices can be used to study and improve sleep quality. In this paper, we utilize the relationship between physical activity and sleep quality to find ways of assisting people improve their sleep using machine learning techniques. People usually have several behavior modes that their bio-functions can be divided into. Performing time series clustering on activity data, we find cluster centers that would correlate to the most evident behavior modes for a specific subject. Activity recipes are then generated for good sleep quality for each behavior mode within each cluster. These activity recipes are supplied to an activity recommendation engine for suggesting a mix of relaxed to intense activities to subjects during their daily routines. The recommendations are further personalized based on the subjects' lifestyle constraints, i.e. their age, gender, body mass index (BMI), resting heart rate, etc, with the objective of the recommendation being the improvement of that night's quality of sleep. This would in turn serve a longer-term health objective, like lowering heart rate, improving the overall quality of sleep, etc.

Co-clustering is a specific type of clustering that addresses the problem of finding groups of objects without necessarily considering all attributes. This technique has shown to have more consistent results in high-dimensional sparse data than traditional clustering. In trajectory co-clustering, the methods found in the literature have two main limitations: first, the space and time dimensions have to be constrained by user-defined thresholds; second, elements (trajectory points) are clustered ignoring the trajectory sequence, assuming that the points are independent among them. To address the limitations above, we propose a new trajectory co-clustering method for mining semantic trajectory co-clusters. It simultaneously clusters the trajectories and their elements taking into account the order in which they appear. This new method uses the element frequency to identify candidate co-clusters. Besides, it uses an objective cost function that automatically drives the co-clustering process, avoiding the need for constraining dimensions. We evaluate the proposed approach using real-world a publicly available dataset. The experimental results show that our proposal finds frequent and meaningful contiguous sequences revealing mobility patterns, thereby the most relevant elements.