Density-based distance metrics have applications in semi-supervised learning, nonlinear interpolation and clustering. We consider density-based metrics induced by Riemannian manifold structures and estimate them using kernel density estimators for the underlying data distribution. We lower bound the rate of convergence of these plug-in path-length estimates and hence of the metric, as the sample size increases. We present an upper bound on the rate of convergence of all estimators of the metric. We also show that the metric can be consistently computed using the shortest path algorithm on a suitably constructed graph on the data samples and lower bound the convergence rate of the computation error. We present experiments illustrating the use of the metrics for semi-supervised classification and non-linear interpolation.

Given a classification problem, our goal is to find a\nlow-dimensional linear transformation of the feature vectors which retains\ninformation needed to predict the class labels. We present a method based on\nmaximum conditional likelihood estimation of mixture models. Use of mixture\nmodels allows us to approximate the distributions to any desired accuracy while\nuse of conditional likelihood as the contrast function ensures that the\nselected subspace retains maximum possible mutual information between feature\nvectors and class labels. Classification experiments using Gaussian mixture\ncomponents show that this method compares favorably to related dimension\nreduction techniques. Other distributions belonging to the exponential family\ncan be used to reduce dimensions when data is of a special type, for example\nbinary or integer valued data. We provide an EM-like algorithm for model\nestimation and present visualization experiments using both the Gaussian and\nthe Bernoulli mixture models.Pre-2018 CSE ID: CS2004-0810

We consider the problem of modeling a distribution whose alphabet size is large relative to the amount of observed data. It is well known that conventional maximum-likelihood estimates do not perform well in that regime. Instead, we find the distribution maximizing the probability of the data's pattern. We derive an efficient algorithm for approximating this distribution. Simulations show that the computed distribution models the data well and yields general estimators that evaluate various data attributes as well as specific estimators designed especially for these tasks

We present a semi-parametric latent variable model based technique for density modelling, dimensionality reduction and visualization. Unlike previous methods, we estimate the latent distribution non-parametrically which enables us to model data generated by an underlying low dimen- sional, multimodal distribution. In addition, we allow the components of latent variable models to be drawn from the exponential family which makes the method suitable for special data types, for example binary or count data. Simulations on real valued, binary and count data show fa- vorable comparison to other related schemes both in terms of separating different populations and generalization to unseen samples.

Multicasting is an efficient means of one to many communication and is typically implemented by creating a multicasting tree. Because of the severe battery power and transmission bandwidth limitations in ad hoc networks, multicast routing can significantly improve the performance of this type of network. However, due to the frequent and hard-to-predict topological changes of ad hoc networks, maintenance of a multicasting tree to ensure its availability could be a difficult task. We borrow from the concept of alternate path routing, which has been studied for providing QoS routing, effective congestion control, security, and route failure protection, to propose a scheme in which a set of multicasting trees is continuously maintained. A tree is used until it fails at which time it is replaced by an alternative tree in the set, so that the time between failure of a tree and resumption of multicast routing is minimal. We introduce the scheme and present a number of heuristics to compute a set of alternate trees. The heuristics are then compared in terms of transmission cost, improvement in the average time between multicast failures and the probability of usefulness. Simulations show significant gains over a wide range of network operational conditions. In particular, we show that using alternate trees has the potential of improving mean time between interruption by 100-600% in a 50 node network (for most multicast group sizes) with small increase in the tree cost and the route discovery overhead.