We explore the effect of dimensionality on the “nearest neighbor” problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and syn...

in this work, one and two-dimensional lattices are studied theoretically by a statistical mechanical approach. the nearest and next-nearest neighbor interactions are both taken into account, and the approximate thermodynamic properties of the lattices are calculated. the results of our calculations show that: (1) even though the next-nearest neighbor interaction may have an insignificant effect...

We present a system for fall detection in which the fall hypothesis, generated on the basis of accelerometric data, is validated by k-NN based classifier operating on depth features. We show that validation of the alarms in such a way leads to lower ratio of false alarms. We demonstrate the detection performance of the system using publicly available data. We discuss algorithms for person detec...

Negative Selection Algorithms (NSAs) have been widely used in anomaly detection. As the security issue becomes more complex, more and more anomaly detection schemes involve high-dimension data. NSAs however perform poorly on effectiveness and efficiency when dealing with high-dimension data. To address these issues, we propose a Neighborhood Negative Selection (NNS) algorithm in this paper. Ins...

We study the collapse transition of a polymer on a square lattice with both nearest-neighbor and next nearest-neighbor interactions, by calculating the exact partition function zeros up to chain length 36. The transition behavior is much more pronounced than that of the model with nearest-neighbor interactions only. The crossover exponent and the transition temperature are estimated from the sc...

We describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting. We show how to maintain, for any positive constant d, a set of n points in R indexed by time such that we can perform insertions or deletions at any point in the timeline in O(log n) amortized time. We support, for any small constant > 0, (1 + )-approximate range rep...

We consider the problem of finding the nearest point in a polyhedral cone C = {x ∈ Rn : Dx ≤ 0} to a given point b ∈ Rn, where D ∈ Rm×n. This problem can be formulated as a convex quadratic programming problem with special structure. We study the structure of this problem and its relationship with the nearest point problem in a pos cone through the concept of polar cones. We then use this relat...

The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest point maps from the perspective of computational algebraic geometry. The Euclidean distance degre...

Throughout the course of several years, significant progress has been made with regard to the accuracy and performance of pair-wise alignment techniques; however when considering low-resolution scans with minimal pairwise overlap, and scans with high levels of symmetry, the process of successfully performing sequential alignments in the object reconstruction process remains a challenging task. ...

We address the problem of novelty detection in multiclass scenarios where some class labels are missing from the training set. Our method is based on the initial assignment of confidence values, which measure the affinity between a new test point and each known class. We first compare the values of the two top elements in this vector of confidence values. In the heart of our method lies the tra...