Related papers: Projection depth for functional data: Practical is…
In machine learning it is common to interpret each data point as a vector in Euclidean space. However the data may actually be functional i.e.\ each data point is a function of some variable such as time and the function is discretely…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
We propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that have considerably different geometric forms or features…
Dimension reduction is often necessary in functional data analysis, with functional principal component analysis being one of the most widely used techniques. A key challenge in applying these methods is determining the number of…
Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
Data depth functions are a generalization of one-dimensional order statistics and medians to real spaces of dimension greater than one; in particular, a data depth function quantifies the centrality of a point with respect to a data set or…
We consider data-based predictive control based on behavioral systems theory. In the linear setting this means that a system is described as a subspace of trajectories, and predictive control can be formulated using a projection onto the…
The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…
Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…
Data depth is an efficient tool for robustly summarizing the distribution of functional data and detecting potential magnitude and shape outliers. Commonly used functional data depth notions, such as the modified band depth and extremal…
We study linear function approximation in a finite basis under finite-precision arithmetic. In a highly non-orthogonal basis, certain directions are only weakly represented, so that rounding errors can significantly distort the effectively…
Depth notions in regression have been systematically proposed and examined in Zuo (2018). One of the prominent advantages of notion of depth is that it can be directly utilized to introduce median-type deepest estimating functionals (or…
This work investigates the ways in which deep learning methods can benefit from random projection (RP), a classic linear dimensionality reduction method. We focus on two areas where, as we have found, employing RP techniques can improve…
In a human-robot collaborative task where a robot helps its partner by finding described objects, the depth dimension plays a critical role in successful task completion. Existing studies have mostly focused on comprehending the object…
The cumulative distribution function (CDF) is fundamental for characterizing random variables, making it essential in applications that require privacy-preserving data analysis. This paper introduces a novel framework for constructing…
This paper develops projection pursuit for discrete data using the discrete Radon transform. Discrete projection pursuit is presented as an exploratory method for finding informative low dimensional views of data such as binary vectors,…
Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a…