Detecting arbitrarily shaped clusters in high-dimensional noisy data is challenging for current clustering methods. We introduce SHADE, the first deep clustering algorithm that incorporates density-connectivity into its loss function. Similar to existing deep clustering algorithms, SHADE supports high-dimensional and large data sets with the expressive power of a deep autoencoder. In contrast to most existing deep clustering methods that rely on a centroid-based clustering objective, SHADE incorporates a novel loss function that captures density-connectivity. It thereby learns a representation that enhances the separation of density-connected clusters. SHADE detects a stable clustering and noise points fully automatically without any user input. It outperforms existing methods in clustering quality, especially on data that contain non-Gaussian clusters, such as video data. Moreover, the embedded space of SHADE is suitable for visualization and interpretation of the clustering results as the individual shapes of the clusters are preserved.

Deep clustering algorithms have gained popularity for clustering complex, large-scale data sets, but getting started is difficult because of numerous decisions regarding architecture, optimizer, and other hyperparameters. Theoretical foundations must be known to obtain meaningful results. At the same time, ease of use is necessary to get used by a broader audience. Therefore, we require a unified framework that allows for easy execution in diverse settings. While this applies to established clustering methods like k-Means and DBSCAN, deep clustering algorithms lack a standard structure, resulting in significant programming overhead. This complicates empirical evaluations, which are essential in both scientific and practical applications. We present a solution to this problem by providing a theoretical background on deep clustering as well as practical implementation techniques and a unified structure with predefined neural networks. For the latter, we use the Python package ClustPy. The aim is to share best practices and facilitate community participation in deep clustering research.

Glass beads were among the most common grave goods in the Early Middle Ages, with an estimated number in the millions. The color, size, shape and decoration of the beads are diverse leading to many different archaeological classification systems that depend on the subjective decisions of individual experts. The lack of an agreed upon expert categorization leads to a pressing problem in archaeology, as the categorization of archaeological artifacts, like glass beads, is important to learn about cultural trends, manufacturing processes or economic relationships (e.g., trade routes) of historical times. An automated, objective and reproducible classification system is therefore highly desirable. We present a high-quality data set of images of Early Medieval beads and propose a clustering pipeline to learn a classification system in a data-driven way. The pipeline consists of a novel extension of deep embedded non-redundant clustering to identify multiple, meaningful clusterings of glass bead images. During the cluster analysis we address several challenges associated with the data and as a result identify high-quality clusterings that overlap with archaeological domain expertise. To the best of our knowledge this is the first application of non-redundant image clustering for archaeological data.

Causal Feature Learning (CFL) infers macro-level causes (e.g., an aggregation of pixels in a traffic light image) from micro-level data (e.g., pixels of the image) by clustering the predicted probabilities of effect states (e.g., state of the traffic light). The current method for CFL uses a two-step procedure. First, a classifier for the effect states is trained, and afterwards, the predicted effect state probabilities are clustered. With CaFe DBSCAN, we present a novel density-based clustering method that conducts CFL directly by estimating conditional probabilities during clustering. To this end, we introduce the notion of clustering regions with similar conditional probabilities of the effect states given their micro-level data points. Our single-step approach has the following benefits: (1) CaFe DBSCAN introduces a comprehensive approach to Causal Feature Learning. Unlike existing methods, CaFe DBSCAN uses a probabilistic framework and does not require separate classification and clustering steps implemented by different algorithms relying on various assumptions, parameter settings, and optimization goals. (2) We do not need to train and tune a classifier first, hence the algorithm is more runtime-efficient than the current approach. (3) Due to the properties of density-based clustering algorithms, CaFe DBSCAN is robust against noise and outliers, which leads to purer clusters. (4) Our algorithm automatically infers a reasonable number of clusters, i.e., macro-level causes. We demonstrate the benefits of CaFe DBSCAN on synthetic and real-world data.

The field of deep clustering combines deep learning and clustering to learn representations that improve both the learned representation and the performance of the considered clustering method. Most existing deep clustering methods are designed for a single clustering method, e.g., k-means, spectral clustering, or Gaussian mixture models, but it is well known that no clustering algorithm works best in all circumstances. Consensus clustering tries to alleviate the individual weaknesses of clustering algorithms by building a consensus between members of a clustering ensemble. Currently, there is no deep clustering method that can include multiple heterogeneous clustering algorithms in an ensemble to update representations and clusterings together. To close this gap, we introduce the idea of a consensus representation that maximizes the agreement between ensemble members. Further, we propose DECCS (Deep Embedded Clustering with Consensus representationS), a deep consensus clustering method that learns a consensus representation by enhancing the embedded space to such a degree that all ensemble members agree on a common clustering result. Our contributions are the following: (1) We introduce the idea of learning consensus representations for heterogeneous clusterings, a novel notion to approach consensus clustering. (2) We propose DECCS, the first deep clustering method that jointly improves the representation and clustering results of multiple heterogeneous clustering algorithms. (3) We show in experiments that learning a consensus representation with DECCS is outperforming several relevant baselines from deep clustering and consensus clustering.

We propose a novel density-based mode-seeking Hierarchical Quick Shift clustering algorithm with an optional Recurrent Neural Network (RNN) to jointly learn the cluster assignments for every sample and the underlying dynamics of the mode-seeking clustering process. As a mode-seeking clustering algorithm, Hierarchical Quick Shift constrains data samples to stay on similar trajectories. All data samples converging to the same local mode are assigned to a common cluster. The RNN enables us to learn quasi-temporal structures during the mode-seeking clustering process. It supports variable density clusters with arbitrary shapes without requiring the expected number of clusters a priori. We evaluate our method in extensive experiments to show the advantages over other density-based clustering algorithms.