We propose K-Deep Simplex (KDS) which, given a set of data points, learns a dictionary comprising synthetic landmarks, along with representation coefficients supported on a simplex. KDS integrates manifold learning and sparse coding/dictionary learning: reconstruction term, as in classical dictionary learning, and a novel local weighted $\ell_1$ penalty that encourages each data point to represent itself as a convex combination of nearby landmarks. We solve the proposed optimization program using alternating minimization and design an efficient, interpretable autoencoder using algorithm enrolling. We theoretically analyze the proposed program by relating the weighted $\ell_1$ penalty in KDS to a weighted $\ell_0$ program. Assuming that the data are generated from a Delaunay triangulation, we prove the equivalence of the weighted $\ell_1$ and weighted $\ell_0$ programs. If the representation coefficients are given, we prove that the resulting dictionary is unique. Further, we show that low-dimensional representations can be efficiently obtained from the covariance of the coefficient matrix. We apply KDS to the unsupervised clustering problem and prove theoretical performance guarantees. Experiments show that the algorithm is highly efficient and performs competitively on synthetic and real data sets.

Topological data analysis (TDA) is an expanding field that leverages principles and tools from algebraic topology to quantify structural features of data sets or transform them into more manageable forms. As its theoretical foundations have been developed, TDA has shown promise in extracting useful information from high-dimensional, noisy, and complex data such as those used in biomedicine. To improve efficiency, these techniques may employ landmark samplers. The heuristic maxmin procedure obtains a roughly even distribution of sample points by implicitly constructing a cover comprising sets of uniform radius. However, issues arise with data that vary in density or include points with multiplicities, as are common in biomedicine. We propose an analogous procedure, "lastfirst" based on ranked distances, which implies a cover comprising sets of uniform cardinality. We first rigorously define the procedure and prove that it obtains landmarks with desired properties. We then perform benchmark tests and compare its performance to that of maxmin, on feature detection and class prediction tasks involving simulated and real-world biomedical data. Lastfirst is more general than maxmin in that it can be applied to any data on which arbitrary (and not necessarily symmetric) pairwise distances can be computed. Lastfirst is more computationally costly, but our implementation scales at the same rate as maxmin. We find that lastfirst achieves comparable performance on prediction tasks and outperforms maxmin on homology detection tasks. Where the numerical values of similarity measures are not meaningful, as in many biomedical contexts, lastfirst sampling may also improve interpretability.

The data collected from a vehicle's Controller Area Network (CAN) can quickly exceed human analysis or annotation capabilities when considering fleets of vehicles, which stresses the importance of unsupervised machine learning methods. This work presents a simultaneous clustering and segmentation approach for vehicle CAN-data that identifies common driving events in an unsupervised manner. The approach builds on self-supervised learning (SSL) for multivariate time series to distinguish different driving events in the learned latent space. We evaluate our approach with a dataset of real Tesla Model 3 vehicle CAN-data and a two-hour driving session that we annotated with different driving events. With our approach, we evaluate the applicability of recent time series-related contrastive and generative SSL techniques to learn representations that distinguish driving events. Compared to state-of-the-art (SOTA) generative SSL methods for driving event discovery, we find that contrastive learning approaches reach similar performance.

World wide transport authorities are imposing complex Hours of Service (from now on, HoS) regulations to drivers (Meyer 2011, Goel and Vidal 2013), which constraint the amount of working, driving and resting time when delivering a service. As a consequence, transport companies are responsible not only of scheduling driving plans aligned with laws that define the legal behaviour of a driver, but also of monitoring and identifying as soon as possible problematic patterns that can incur in costs due to sanctions. Fortunately, the widespread adoption of onboard IoT devices in vehicle fleets enables recording of the driver activities in event logs, but the large amount of data ingested makes difficult for transport experts to understand what happened and to make actions that forestall illegal behaviour. For this reason, an important technical challenge is to come up with easily interpretable descriptive models that help understand the huge amount of information stored in such event logs. The main objective not only consists of finding out if drivers workplan complies with the HoS regulation, but also summarising their activities in a concise but representative way. Additionally, these underlying patterns in the event log could be analysed in order to discover driving styles which could make possible the suggestion of routes or tasks more aligned to the driver preferences. The creation of driver profiles based on driving styles with HoS can be extremely useful for managers, as they could assign transport routes to the most appropriate drivers, given the length of the route and the proximity of the deadline. For example, drivers who maximise their driving hours could be preferred for long distance routes and drivers who tend to take split rest to on-city deliveries.

We consider a semi-supervised $k$-clustering problem where information is available on whether pairs of objects are in the same or in different clusters. This information is either available with certainty or with a limited level of confidence. We introduce the PCCC algorithm, which iteratively assigns objects to clusters while accounting for the information provided on the pairs of objects. Our algorithm can include relationships as hard constraints that are guaranteed to be satisfied or as soft constraints that can be violated subject to a penalty. This flexibility distinguishes our algorithm from the state-of-the-art in which all pairwise constraints are either considered hard, or all are considered soft. Unlike existing algorithms, our algorithm scales to large-scale instances with up to 60,000 objects, 100 clusters, and millions of cannot-link constraints (which are the most challenging constraints to incorporate). We compare the PCCC algorithm with state-of-the-art approaches in an extensive computational study. Even though the PCCC algorithm is more general than the state-of-the-art approaches in its applicability, it outperforms the state-of-the-art approaches on instances with all hard constraints or all soft constraints both in terms of running time and various metrics of solution quality. The source code of the PCCC algorithm is publicly available on GitHub.

The mining and exploitation of graph structural information have been the focal points in the study of complex networks. Traditional structural measures in Network Science focus on the analysis and modelling of complex networks from the perspective of network structure, such as the centrality measures, the clustering coefficient, and motifs and graphlets, and they have become basic tools for studying and understanding graphs. In comparison, graph neural networks, especially graph convolutional networks (GCNs), are particularly effective at integrating node features into graph structures via neighbourhood aggregation and message passing, and have been shown to significantly improve the performances in a variety of learning tasks. These two classes of methods are, however, typically treated separately with limited references to each other. In this work, aiming to establish relationships between them, we provide a network science perspective of GCNs. Our novel taxonomy classifies GCNs from three structural information angles, i.e., the layer-wise message aggregation scope, the message content, and the overall learning scope. Moreover, as a prerequisite for reviewing GCNs via a network science perspective, we also summarise traditional structural measures and propose a new taxonomy for them. Finally and most importantly, we draw connections between traditional structural approaches and graph convolutional networks, and discuss potential directions for future research.

We present an unsupervised data processing workflow that is specifically designed to obtain a fast conformational clustering of long molecular dynamics simulation trajectories. In this approach we combine two dimensionality reduction algorithms (cc\_analysis and encodermap) with a density-based spatial clustering algorithm (HDBSCAN). The proposed scheme benefits from the strengths of the three algorithms while avoiding most of the drawbacks of the individual methods. Here the cc\_analysis algorithm is for the first time applied to molecular simulation data. Encodermap complements cc\_analysis by providing an efficient way to process and assign large amounts of data to clusters. The main goal of the procedure is to maximize the number of assigned frames of a given trajectory, while keeping a clear conformational identity of the clusters that are found. In practice we achieve this by using an iterative clustering approach and a tunable root-mean-square-deviation-based criterion in the final cluster assignment. This allows to find clusters of different densities as well as different degrees of structural identity. With the help of four test systems we illustrate the capability and performance of this clustering workflow: wild-type and thermostable mutant of the Trp-cage protein (TC5b and TC10b), NTL9 and Protein B. Each of these systems poses individual challenges to the scheme, which in total give a nice overview of the advantages, as well as potential difficulties that can arise when using the proposed method.

Deep learning methods in the literature are commonly benchmarked on image data sets, which may not be suitable or effective baselines for non-image tabular data. In this paper, we take a data-centric view to perform one of the first studies on deep embedding clustering of tabular data. Eight clustering and state-of-the-art embedding clustering methods proposed for image data sets are tested on seven tabular data sets. Our results reveal that a traditional clustering method ranks second out of eight methods and is superior to most deep embedding clustering baselines. Our observation aligns with the literature that conventional machine learning of tabular data is still a robust approach against deep learning. Therefore, state-of-the-art embedding clustering methods should consider data-centric customization of learning architectures to become competitive baselines for tabular data.

Contrastive deep clustering has recently gained significant attention with its ability of joint contrastive learning and clustering via deep neural networks. Despite the rapid progress, previous works mostly require both positive and negative sample pairs for contrastive clustering, which rely on a relative large batch-size. Moreover, they typically adopt a two-stream architecture with two augmented views, which overlook the possibility and potential benefits of multi-stream architectures (especially with heterogeneous or hybrid networks). In light of this, this paper presents a new end-to-end deep clustering approach termed Heterogeneous Tri-stream Clustering Network (HTCN). The tri-stream architecture in HTCN consists of three main components, including two weight-sharing online networks and a target network, where the parameters of the target network are the exponential moving average of that of the online networks. Notably, the two online networks are trained by simultaneously (i) predicting the instance representations of the target network and (ii) enforcing the consistency between the cluster representations of the target network and that of the two online networks. Experimental results on four challenging image datasets demonstrate the superiority of HTCN over the state-of-the-art deep clustering approaches. The code is available at https://github.com/dengxiaozhi/HTCN.

Representation learning is important for solving sequence-to-sequence problems in natural language processing. Representation learning transforms raw data into vector-form representations while preserving their features. However, data with significantly different features leads to heterogeneity in their representations, which may increase the difficulty of convergence. We design a multi-filter encoder-decoder model to resolve the heterogeneity problem in sequence-to-sequence tasks. The multi-filter model divides the latent space into subspaces using a clustering algorithm and trains a set of decoders (filters) in which each decoder only concentrates on the features from its corresponding subspace. As for the main contribution, we design a self-enhancing mechanism that uses a reinforcement learning algorithm to optimize the clustering algorithm without additional training data. We run semantic parsing and machine translation experiments to indicate that the proposed model can outperform most benchmarks by at least 5\%. We also empirically show the self-enhancing mechanism can improve performance by over 10\% and provide evidence to demonstrate the positive correlation between the model's performance and the latent space clustering.