In this paper we propose an active metric learning method for clustering with pairwise constraints. The proposed method actively queries the label of informative instance pairs, while estimating underlying metrics by incorporating unlabeled instance pairs, which leads to a more accurate and efficient clustering process. In particular, we augment the queried constraints by generating more pairwise labels to provide additional information in learning a metric to enhance clustering performance. Furthermore, we increase the robustness of metric learning by updating the learned metric sequentially and penalizing the irrelevant features adaptively. In addition, we propose a novel active query strategy that evaluates the information gain of instance pairs more accurately by incorporating the neighborhood structure, which improves clustering efficiency without extra labeling cost. In theory, we provide a tighter error bound of the proposed metric learning method utilizing augmented queries compared with methods using existing constraints only. Furthermore, we also investigate the improvement using the active query strategy instead of random selection. Numerical studies on simulation settings and real datasets indicate that the proposed method is especially advantageous when the signal-to-noise ratio between significant features and irrelevant features is low.

The in-memory algorithms for approximate nearest neighbor search (ANNS) have achieved great success for fast high-recall search, but are extremely expensive when handling very large scale database. Thus, there is an increasing request for the hybrid ANNS solutions with small memory and inexpensive solid-state drive (SSD). In this paper, we present a simple but efficient memory-disk hybrid indexing and search system, named SPANN, that follows the inverted index methodology. It stores the centroid points of the posting lists in the memory and the large posting lists in the disk. We guarantee both disk-access efficiency (low latency) and high recall by effectively reducing the disk-access number and retrieving high-quality posting lists. In the index-building stage, we adopt a hierarchical balanced clustering algorithm to balance the length of posting lists and augment the posting list by adding the points in the closure of the corresponding clusters. In the search stage, we use a query-aware scheme to dynamically prune the access of unnecessary posting lists. Experiment results demonstrate that SPANN is 2$\times$ faster than the state-of-the-art ANNS solution DiskANN to reach the same recall quality $90\%$ with same memory cost in three billion-scale datasets. It can reach $90\%$ recall@1 and recall@10 in just around one millisecond with only 32GB memory cost. Code is available at: {\footnotesize\color{blue}{\url{https://github.com/microsoft/SPTAG}}}.

Proximity measures on graphs have a variety of applications in network analysis, including community detection. Previously they have been mainly studied in the context of networks without attributes. If node attributes are taken into account, however, this can provide more insight into the network structure. In this paper, we extend the definition of some well-studied proximity measures to attributed networks. To account for attributes, several attribute similarity measures are used. Finally, the obtained proximity measures are applied to detect the community structure in some real-world networks using the spectral clustering algorithm.

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.