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The curse of dimensionality in the realm of association rules is twofold. Firstly, we have the well known exponential increase in computational complexity with increasing item set size. Secondly, there is a \emph{related curse} concerned…

With the rising applications implemented in different domains, it is inevitable to require databases to adopt corresponding appropriate data models to store and exchange data derived from various sources. To handle these data models in a…

This study addresses the challenge of accurately identifying multi-task contention types in high-dimensional system environments and proposes a unified contention classification framework that integrates representation transformation,…

We consider statistical inference in high-dimensional regression problems under affine constraints on the parameter space. The theoretical study of this is motivated by the study of genetic determinants of diseases, such as diabetes, using…

Cluster analysis of very high dimensional data can benefit from the properties of such high dimensionality. Informally expressed, in this work, our focus is on the analogous situation when the dimensionality is moderate to small, relative…

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data.…

Multiple instance data are sets or multi-sets of unordered elements. Using metrics or distances for sets, we propose an approach to several multiple instance learning tasks, such as clustering (unsupervised learning), classification…

Data cleaning is a long-standing challenge in data management. While powerful logic and statistical algorithms have been developed to detect and repair data errors in tables, existing algorithms predominantly rely on domain-experts to first…

When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…

How to extract useful insights from data is always a challenge, especially if the data is multidimensional. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or…

The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…

Practically all of the planning research is limited to states represented in terms of Boolean and numeric state variables. Many practical problems, for example, planning inside complex software systems, require far more complex data types,…

Data constraints are fundamental for practical data modelling, and a verifiable conformance of a data instance to a safety-critical constraint (satisfaction relation) is a corner-stone of safety assurance. Diagrammatic constraints are…

The non-trivial structure of such complex systems makes the analysis of their collective behavior a challenge. The problem is even more difficult when the information is distributed across networks (e.g., communication networks in different…

This paper rigorously and concisely defines, in the context of our (Elementary) Mathematical Data Model ((E)MDM), the mathematical concepts of self-map, composite mapping, totality, one-to-oneness, non-primeness, ontoness, bijectivity,…

In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…

Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…

Data Mining is a promising field and is applied in multiple domains for its predictive capabilities. Data in the real world cannot be readily used for data mining as it suffers from the problems of multidimensionality, unbalance and missing…

Object counting models suffer when deployed across domains with differing density variety, since density shifts are inherently task-relevant and violate standard domain adaptation assumptions. To address this, we propose a theoretical…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…