Alexander Bernstein

Incremental Construction of Low-Dimensional Data Representations

Various Dimensionality Reduction algorithms transform initial high-dimensional data into their lower-dimensional representations preserving chosen properties of the initial data. Typically, such algorithms use the solution of large-dimensional optimization problems, and the incremental versions are designed for many popular algorithms to reduce their computational complexity. Under manifold assumption about high-dimensional data, advanced manifold learning algorithms should preserve the Data manifold and its differential properties such as tangent spaces, Riemannian tensor, etc. Incremental version of the Grassmann&Stiefel Eigenmaps manifold learning algorithm, which has asymptotically minimal reconstruction error, is proposed in this paper and has significantly smaller computational complexity in contrast to the initial algorithm.

Statistical Learning on Manifold-Valued Data

Regression on manifolds problem is to estimate an unknown smooth function f that maps p-dimensional manifold-valued inputs, whose values lie on unknown Input manifold M of lower dimensionality q < p embedded in an ambient high-dimensional input space Rp, to m-dimensional outputs from training sample consisting of given ‘input-output’ pairs. We consider this problem in which Jacobian Jf(X) of function f and Input manifold M should be also estimated. The paper presents a new geometrically motivated method for estimating a triple (f(X), Jf(X), M) from given sample. The proposed solution is based on solving a Tangent bundle manifold learning problem for specific unknown Regression manifold embedded in input-output space Rp+m and consisting of input-output pairs (X, f(X)), X ∈ M.

Mobile Robot Localization via Machine Learning

We consider an appearance-based robot self-localization problem in the machine learning framework. Using recent manifold learning techniques, we propose a new geometrically motivated solution. The solution includes estimation of the robot localization mapping from the appearance manifold to the robot localization space, as well as estimation of the inverse mapping for image modeling. The latter allows solving the robot localization problem as a Kalman filtering problem.

Nonlinear multi-output regression on unknown input manifold

Consider unknown smooth function which maps high-dimensional inputs to multidimensional outputs and whose domain of definition is unknown low-dimensional input manifold embedded in an ambient high-dimensional input space. Given training dataset consisting of ‘input-output’ pairs, regression on input manifold problem is to estimate the unknown function and its Jacobian matrix, as well to estimate the input manifold. By transforming high-dimensional inputs in their low-dimensional features, initial regression problem is reduced to certain regression on feature space problem. The paper presents a new geometrically motivated method for solving both interrelated regression problems.

Optimal filtering of a random background in image processing problems

We describe a recurrent construction procedure for mean-square optimal linear spatio-temporal filtering of a random background, which makes it possible to construct filtered frames using explicitly written compact analytical expressions.

Reinforcement Learning for Computer Vision and Robot Navigation

Nowadays, machine learning has become one of the basic technologies used in solving various computer vision tasks such as feature detection, image segmentation, object recognition and tracking. In many applications, various complex systems such as robots are equipped with visual sensors from which they learn the state of a surrounding environment by solving corresponding computer vision tasks. Solutions of these tasks are used for making decisions about possible future actions. Reinforcement learning is one of the modern machine learning technologies in which learning is carried out through interaction with the environment. In recent years, reinforcement learning has been used both for solving robotic computer vision problems such as object detection, visual tracking and action recognition as well as robot navigation. The paper describes shortly the reinforcement learning technology and its use for computer vision and robot navigation problems.

Reinforcement learning in computer vision

Nowadays, machine learning has become one of the basic technologies used in solving various computer vision tasks such as feature detection, image segmentation, object recognition and tracking. In many applications, various complex systems such as robots are equipped with visual sensors from which they learn state of surrounding environment by solving corresponding computer vision tasks. Solutions of these tasks are used for making decisions about possible future actions. It is not surprising that when solving computer vision tasks we should take into account special aspects of their subsequent application in model-based predictive control. Reinforcement learning is one of modern machine learning technologies in which learning is carried out through interaction with the environment. In recent years, Reinforcement learning has been used both for solving such applied tasks as processing and analysis of visual information, and for solving specific computer vision problems such as filtering, extracting image features, localizing objects in scenes, and many others. The paper describes shortly the Reinforcement learning technology and its use for solving computer vision problems.

Manifold Learning Regression with Non-stationary Kernels

Nonlinear multi-output regression problem is to construct a predictive function which estimates an unknown smooth mapping from q-dimensional inputs to m-dimensional outputs based on a training data set consisting of given “input-output” pairs. In order to solve this problem, regression models based on stationary kernels are often used. However, such approaches are not efficient for functions with strongly varying gradients. There exist some attempts to introduce non-stationary kernels to account for possible non-regularities, although even the most efficient one called Manifold Learning Regression (MLR), which estimates the unknown function as well its Jacobian matrix, is too computationally expensive. The main problem is that the MLR is based on a computationally intensive manifold learning technique. In this paper we propose a modified version of the MLR with significantly less computational complexity while preserving its accuracy.

Pattern Recognition Pipeline for Neuroimaging Data

As machine learning continues to gain momentum in the neuroscience community, we witness the emergence of novel applications such as diagnostics, characterization, and treatment outcome prediction for psychiatric and neurological disorders, for instance, epilepsy and depression. Systematic research into these mental disorders increasingly involves drawing clinical conclusions on the basis of data-driven approaches; to this end, structural and functional neuroimaging serve as key source modalities. Identification of informative neuroimaging markers requires establishing a comprehensive preparation pipeline for data which may be severely corrupted by artifactual signal fluctuations. We propose a new unified data analysis pipeline for neuroimaging-based diagnostic classification problems using various different feature extraction techniques, Machine Learning algorithms and processing toolboxes for brain imaging. We illustrate the approach by discovering potential candidates for new biomarkers for diagnostics of epilepsy and depression presence in simple and complex cases based on clinical and MRI data for patients and healthy volunteers. We also demonstrate that the proposed pipeline in many classification tasks provides better performance than conventional ones.

Machine vision and appearance based learning

Smart algorithms are used in Machine vision to organize or extract high-level information from the available data. The resulted high-level understanding the content of images received from certain visual sensing system and belonged to an appearance space can be only a key first step in solving various specific tasks such as mobile robot navigation in uncertain environments, road detection in autonomous driving systems, etc. Appearance-based learning has become very popular in the field of machine vision. In general, the appearance of a scene is a function of the scene content, the lighting conditions, and the camera position. Mobile robots localization problem in machine learning framework via appearance space analysis is considered. This problem is reduced to certain regression on an appearance manifold problem, and newly regression on manifolds methods are used for its solution.