Related papers: Random projections for curves in high dimensions
We study the $k$-median clustering problem for high-dimensional polygonal curves with finite but unbounded number of vertices. We tackle the computational issue that arises from the high number of dimensions by defining a…
The Fr\'echet distance is a popular distance measure for curves which naturally lends itself to fundamental computational tasks, such as clustering, nearest-neighbor searching, and spherical range searching in the corresponding metric…
The Fr\'echet distance is a computational mainstay for comparing polygonal curves. The Fr\'echet distance under translation, which is a translation invariant version, considers the similarity of two curves independent of their location in…
The Fr\'echet distance is a popular similarity measure that is well-understood for polygonal curves in $\mathbb{R}^d$: near-quadratic time algorithms exist, and conditional lower bounds suggest that these results cannot be improved…
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…
We study data structures for storing a set of polygonal curves in ${\rm R}^d$ such that, given a query curve, we can efficiently retrieve similar curves from the set, where similarity is measured using the discrete Fr\'echet distance or the…
The discrete Fr\'echet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fr\'echet distance under translation, which enables detection of similar movement patterns in different spatial…
The \emph{Fr\'echet distance} is a well studied similarity measures between curves. The \emph{discrete Fr\'echet distance} is an analogous similarity measure, defined for a sequence $A$ of $m$ points and a sequence $B$ of $n$ points, where…
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 similarity of two polygonal curves can be measured using the Fr\'echet distance. We introduce the notion of a more robust Fr\'echet distance, where one is allowed to shortcut between vertices of one of the curves. This is a natural…
We propose sublinear algorithms for probabilistic testing of the discrete and continuous Fr\'echet distance - a standard similarity measure for curves. We assume the algorithm is given access to the input curves via a query oracle: a query…
The Fr\'echet distance is a well-studied and very popular measure of similarity of two curves. The best known algorithms have quadratic time complexity, which has recently been shown to be optimal assuming the Strong Exponential Time…
Consider the natural question of how to measure the similarity of curves in the plane by a quantity that is invariant under translations of the curves. Such a measure is justified whenever we aim to quantify the similarity of the curves'…
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…
The discrete Fr{\'e}chet distance is a measure of similarity between point sequences which permits to abstract differences of resolution between the two curves, approximating the original Fr{\'e}chet distance between curves. Such distance…
The Fr\'{e}chet distance is a well studied and commonly used measure to capture the similarity of polygonal curves. Unfortunately, it exhibits a high sensitivity to the presence of outliers. Since the presence of outliers is a frequently…
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Fr\'echet regression is becoming a mainstay in modern data analysis for analyzing non-traditional data types belonging to general metric spaces. This novel regression method is especially useful in the analysis of complex health data such…
Given two simplicial complexes in R^d, and start and end vertices in each complex, we show how to compute curves (in each complex) between these vertices, such that the Fr\'echet distance between these curves is minimized. As a polygonal…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…