Cluster tracing algorithms are used to mine temporal evolutions of clusters. Generally, clusters represent groups of objects with similar values. In a temporal context like tracing, similar values correspond to similar behavior in one snapshot in time. Recently, tracing based on object-value-similarity was introduced. In this new paradigm, the decision whether two clusters are considered similar is based on the similarity of the clusters' object values. Existing approaches of this paradigm, however, have a severe limitation. The mapping of clusters between snapshots in time is performed pairwise, i.e. global connections between a temporal snapshot's clusters are ignored; thus, impacts of other clusters that may affect the mapping are not considered and incorrect cluster tracings may be obtained.

Mining temporal multivariate data by clustering is an important research topic. In today's complex data, interesting patterns are often neither bound to the whole dimensional nor temporal extent of the data domain. This challenge is met by temporal subspace clustering methods. Their effectiveness, however, is impeded by aspects unavoidable in real world data: Misalignments between time series, for example caused by out-of-sync sensors, and measurement errors. Under these conditions, existing temporal subspace clustering approaches miss the patterns contained in the data. In this paper, we propose a novel clustering method that mines temporal subspace clusters reflected by sets of objects and relevant intervals. We enable flexible handling of misaligned time series by adaptively shifting time series in the time domain, and we achieve robustness to measurement errors by allowing certain fractions of deviating values in each relevant point in time. We show the effectiveness of our method in experiments on real and synthetic data.

Analysis of temporal climate data is an active research area. Advanced data mining methods designed especially for these temporal data support the domain expert’s pursuit to understand phenomena as the climate change, which is crucial for a sustainable world. Important solutions for mining temporal data are cluster tracing approaches, which are used to mine temporal evolutions of clusters. Generally, clusters represent groups of objects with similar values. In a temporal context like tracing, similar values correspond to similar behavior in one snapshot in time. Each cluster can be interpreted as a behavior type and cluster tracing corresponds to tracking similar behaviors over time. Existing tracing approaches are for datasets satisfying two specific conditions: The clusters appear in all attributes, i.e., fullspace clusters , and the data objects have unique identifiers. These identifiers are used for tracking clusters by measuring the number of objects two clusters have in common, i.e. clusters are traced based on similar object sets . These conditions, however, are strict: First, in complex data, clusters are often hidden in individual subsets of the dimensions . Second, mapping clusters based on similar objects sets does not reflect the idea of tracing similar behavior types over time, because similar behavior can even be represented by clusters having no objects in common. A tracing method based on similar object values is needed. In this paper, we introduce a novel approach that traces subspace clusters based on object value similarity . Neither subspace tracing nor tracing by object value similarity has been done before.

Fast similarity search in high dimensional feature spaces is crucial in today's applications. Since the performance of traditional index structures degrades with increasing dimensionality, concepts were developed to cope with this curse of dimensionality. Most of the existing concepts exploit global correlations between dimensions to reduce the dimensionality of the feature space. In high dimensional data, however, correlations are often locally constrained to a subset of the data and every object can participate in several of these correlations. Accordingly, discarding the same set of dimensions for each object based on global correlations and ignoring the different correlations of single objects leads to significant loss of information. These aspects are relevant due to the direct correspondence between the degree of information preserved and the achievable query performance.

Due to the ever growing presence of data streams, there has been a considerable amount of research on stream mining algorithms. While many algorithms have been introduced that tackle the problem of clustering on evolving data streams, hardly any attention has been paid to appropriate evaluation measures. Measures developed for static scenarios, namely structural measures and ground-truth-based measures, cannot correctly reflect errors attributable to emerging, splitting, or moving clusters. These situations are inherent to the streaming context due to the dynamic changes in the data distribution. In this paper we develop a novel evaluation measure for stream clustering called Cluster Mapping Measure (CMM). CMM effectively indicates different types of errors by taking the important properties of evolving data streams into account. We show in extensive experiments on real and synthetic data that CMM is a robust measure for stream clustering evaluation.

Detecting emerging problems in information and manufacturing systems is the goal of monitoring tools. Good and timely detection of problematic conditions from measured indicators requires efficient and effective detection of critical patterns in a stream of incoming observations.

Analyzing uncertain databases is a challenge in data mining research. Usually, data mining methods rely on precise values. In scenarios where uncertain values occur, e.g. due to noisy sensor readings, these algorithms cannot deliver high-quality patterns. Beside uncertainty, data mining methods face another problem: high dimensional data. For finding object groupings with locally relevant dimensions in this data, subspace clustering was introduced. For high dimensional uncertain data, however, deciding whether dimensions are relevant for a subspace cluster is even more challenging; thus, approaches for effective subspace clustering on uncertain databases are needed. In this paper, we develop a method for subspace clustering for uncertain data that delivers high-quality patterns; the information provided by the individual distributions of objects is used in an effective manner. Because in uncertain scenarios a strict assignment of objects to single clusters is not appropriate, we enrich our model with the concept of membership degree. Subspace clustering for uncertain data is computationally expensive; thus, we propose an efficient algorithm. In thorough experiments we show the effectiveness and efficiency of our new subspace clustering method.

Large data resources are ubiquitous in science and business. For these domains, an intuitive view on the data is essential to fully exploit the hidden knowledge. Often, these data can be semantically structured by concepts. Since the determination of concepts requires a thorough analysis of the data, data mining methods have to be applied. In the field of subspace clustering, some techniques have recently shown to be effective for this task. Although these methods generate concept-based patterns, the user has to provide domain knowledge to gain reasonable concepts out of the data. Our demonstration CoDA (Concept Determination and Analysis) is a tool that supports the user in the final step of concept definition. More concretely, the user is guided through an iterative, interactive process in which concepts are suggested, analyzed, and potentially refined. The core aspect of CoDA is an intuitive, concept-driven presentation of subspace clusters such that concepts can be visually captured.

Time series arise in many different applications in the form of sensor data, stocks data, videos, and other time-related information. Analysis of this data typically requires searching for similar time series in a database. Dynamic Time Warping (DTW) is a widely used high-quality distance measure for time series. As DTW is computationally expensive, efficient algorithms for fast computation are crucial. In this paper, we propose a novel filter-and-refine DTW algorithm called Anticipatory DTW. Existing algorithms aim at efficiently finding similar time series by filtering the database and computing the DTW in the refinement step. Unlike these algorithms, our approach exploits previously unused information from the filter step during the refinement, allowing for faster rejection of false candidates. We characterize a class of applicable filters for our approach, which comprises state-of-the-art lower bounds of the DTW. Our novel anticipatory pruning incurs hardly any over-head and no false dismissals. We demonstrate substantial efficiency improvements in thorough experiments on synthetic and real world time series databases and show that our technique is highly scalable to multivariate, long time series and wide DTW bands.