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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…
Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the…
The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. This dissertation systematically trailblazes a novel volumetric modeling framework to…
A graph is a data structure composed of dots (i.e. vertices) and lines (i.e. edges). The dots and lines of a graph can be organized into intricate arrangements. The ability for a graph to denote objects and their relationships to one…
Mechanics studies the relationships between space, time, and matter, which can be expressed in terms of the dimensions of length $\mathcal{L}$, time $\mathcal{T}$, and mass $\mathcal{M}$. Each dimension broadens the scope of mechanics, from…
Stochastic differential equations have been an important tool in modeling complex financial relations, equipped with the possibility of being multidimensional to better oversee complexities inherent in finance. This multidimensionality,…
Despite their ubiquity, authoring dashboards for metrics reporting in modern data analysis tools remains a manual, time-consuming process. Rather than focusing on interesting combinations of their data, users have to spend time creating…
We present the multidimensional membership mixture (M3) models where every dimension of the membership represents an independent mixture model and each data point is generated from the selected mixture components jointly. This is helpful…
Dimensionality reduction is used as an important tool for unraveling the complexities of high-dimensional datasets in many fields of science, such as cell biology, chemical informatics, and physics. Visualizations of the dimensionally…
Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…
We consider the problem of representing multidimensional data where the domain of each dimension is organized hierarchically, and the queries require summary information at a different node in the hierarchy of each dimension. This is the…
As XML becomes ubiquitous and XML storage and processing becomes more efficient, the range of use cases for these technologies widens daily. One promising area is the integration of XML and data warehouses, where an XML-native database…
Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably…
Fractal dimension is an effective scaling exponent of characterizing scale-free phenomena such as cities. Urban growth can be described with time series of fractal dimension of urban form. However, how to explain the factors behind fractal…
Understanding large amounts of spatiotemporal data from particle-based simulations, such as molecular dynamics, often relies on the computation and analysis of aggregate measures. These, however, by virtue of aggregation, hide structural…
We present Column2Vec, a distributed representation of database columns based on column metadata. Our distributed representation has several applications. Using known names for groups of columns (i.e., a table name), we train a model to…
There are several notions of the 'dual' of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselves to the case of two letters/tiles. Furthermore, we obtain…
We present a data model describing the structure of spectrophotometric datasets with spectral and temporal coordinates and associated metadata. This data model may be used to represent spectra, time series data, segments of SED (Spectral…
Text documents are complex high dimensional objects. To effectively visualize such data it is important to reduce its dimensionality and visualize the low dimensional embedding as a 2-D or 3-D scatter plot. In this paper we explore…
Implicit copulas are the most common copula choice for modeling dependence in high dimensions. This broad class of copulas is introduced and surveyed, including elliptical copulas, skew $t$ copulas, factor copulas, time series copulas and…