Isometry Blind Dynamic Time Warping (IBDTW)
In this work, we explore the problem of aligning two time-ordered point clouds which are spatially transformed and re-parameterized versions of each other. This has a diverse array of applications such as cross modal time series synchronization (e.g. MOCAP to video) and alignment of discretized curves in images. Most other works that address this problem attempt to jointly uncover a spatial alignment and correspondences between the two point clouds, or to derive local invariants to spatial transformations such as curvature before computing correspondences. By contrast, we sidestep spatial alignment completely by using self-similarity matrices (SSMs) as a proxy to the time-ordered point clouds, since self-similarity matrices are blind to isometries and respect global geometry. Our algorithm, dubbed ‘Isometry Blind Dynamic Time Warping’ (IBDTW), is simple and general, and we show that its associated dissimilarity measure lower bounds the L1 Gromov-Hausdorff distance between the two point sets when restricted to warping paths. We also present a local, partial alignment extension of IBDTW based on the Smith Waterman algorithm. This eliminates the need for tedious manual cropping of time series, which is ordinarily necessary for global alignment algorithms to function properly. …

Network Vector
We propose a neural embedding algorithm called Network Vector, which learns distributed representations of nodes and the entire networks simultaneously. By embedding networks in a low-dimensional space, the algorithm allows us to compare networks in terms of structural similarity and to solve outstanding predictive problems. Unlike alternative approaches that focus on node level features, we learn a continuous global vector that captures each node’s global context by maximizing the predictive likelihood of random walk paths in the network. Our algorithm is scalable to real world graphs with many nodes. We evaluate our algorithm on datasets from diverse domains, and compare it with state-of-the-art techniques in node classification, role discovery and concept analogy tasks. The empirical results show the effectiveness and the efficiency of our algorithm. …

Parametric Model
In statistics, a parametric model or parametric family or finite-dimensional model is a family of distributions that can be described using a finite number of parameters. These parameters are usually collected together to form a single k-dimensional parameter vector θ = (θ1, θ2, …, θk). Parametric models are contrasted with the semi-parametric, semi-nonparametric, and non-parametric models, all of which consist of an infinite set of ‘parameters’ for description. The distinction between these four classes is as follows:
• in a ‘parametric’ model all the parameters are in finite-dimensional parameter spaces;
• a model is ‘non-parametric’ if all the parameters are in infinite-dimensional parameter spaces;
• a ‘semi-parametric’ model contains finite-dimensional parameters of interest and infinite-dimensional nuisance parameters;
• a ‘semi-nonparametric’ model has both finite-dimensional and infinite-dimensional unknown parameters of interest.
Some statisticians believe that the concepts ‘parametric’, ‘non-parametric’, and ‘semi-parametric’ are ambiguous. It can also be noted that the set of all probability measures has cardinality of continuum, and therefore it is possible to parametrize any model at all by a single number in (0,1) interval. This difficulty can be avoided by considering only ‘smooth’ parametric models. …