SBIR-STTR Award

Signal Innovations Group proposes a hierarchical Bayesian approach for non-linear dimensionality reduction that addresses three key challenges: learning a reversible mapping from a high-dimensional observed space to a low-dimensional embedded space, learning the dimension of the embedded space, and generating new high-dimensional data for a given location in the embedded space. The proposed generative approach is statistical and jointly learns the probabilistic reversible mapping and the dimension of the embedded space. The proposed approach also enables new high-dimensional data to be embedded in a previously learned low-dimensional space. A hierarchical Bayesian method is also proposed to learn a non-linear dynamic model in the low-dimensional space, allowing joint analysis of multiple types of dynamic data, synthesis of new dynamic data in the low-dimensional space, and mapping synthesized data to the high-dimensional observation space. The models are designed to uncover the relevant characteristics and structure of data through non-linear dimensionality reduction, which enables a human analyst to identify and explore the characteristics in the low-dimensional manifold space and generate new unobserved high-dimensional data.

Benefit:
A diverse array of fields, including image and signal processing, computer vision, speech and pattern recognition, and data mining, have interest in data of very high dimension. Common tasks, such as object detection and classification, image segmentation, pose estimation, motion tracking, and social network analysis, can benefit from manifold learning and non-linear dimensionality reduction. Furthermore, the ability to investigate and characterize high-dimensional data through a low-dimensional embedded space can lead to a better understanding of the relevant features and limitations of the data, help define requirements for additional data collection, and even guide future sensor development. Many applications, such as target recognition, require the collection of significant amounts of data for learning the recognition models. Data collection can be a costly exercise, and available data is often limited and not fully representative of target characteristics and environmental conditions that may be encountered in the future. By exploring the low-dimensional embedded space, an analyst can identify critical features for a given task and/or features that are not sufficiently sampled by the current data. Generating new high-dimensional data from the current low-dimensional embedding is an efficient and inexpensive way to augment the collected data, resolve critical feature regions on the manifold, and adaptively acquire more relevant data as new environments are encountered. The technology developed under this SBIR can have significant impact on a broad spectrum of DoD, intelligence, and private sector applications. The proposed technology may be used for DoD-related target detection and recognition applications, including radar, sonar, and EO/IR sensor platforms. The proposed technology has the potential to significantly improve social network analysis and inference. The military and intelligence communities require methods to estimate the state of social, political, economic, and infrastructure networks that are encountered in counter-insurgency and counter-terrorism operations and analyses. The proposed technology may be applied to characterize and understand the overwhelming sources of information, features, and attributes of a network, as well as generate reduced dimensionality representations for network segmentation. The availability of high spatial and spectral resolution satellite imagery has created a growth industry in applications such as land-use assessment, optimized natural resource extraction, habitat analysis, and precision agriculture. However, the huge volume of data that must be collected, transferred, and processed limits the utility of the imagery. By mapping the data to a low-dimensional space that still retains the relevant information, the proposed techniques can be utilized for data compression. The proposed techniques for manifold learning and dynamic modeling and synthesis can benefit public safety and security applications that exploit fixed and mobile image and video analytics. Specific applications include passenger and pedestrian detection and monitoring in transit terminals, suspicious object detection, and anomalous behavior detection through pose estimation and motion tracking. Estimates have shown a tenfold market increase over 5 years for automated security surveillance alone, from $68 million in 2004 to $840 million in 2009. Other potential markets include mining of surveillance cameras for retail applications and targeted advertising by automatically mining social network data and video content, including online video (e.g. YouTube) and network television.

Keywords:
Nonlinear dimensionality reduction, Nonlinear dimensionality reduction, data synthesis, mixture of factor analyzers, Bayesian nonparametric methods, Manifold learning

Signal Innovations Group (SIG) proposes a Phase II program that addresses three primary capabilities for applications involving high-dimensional observed data: reversible nonlinear data dimensionality reduction, static and dynamic synthesis of data in the observed space based on a low-dimensional latent space, and intuitive and meaningful human interaction with the data in both the observed and latent spaces. Each of these three capabilities will be addressed in the Phase II Base effort through the development of models and algorithms, visualization techniques, and a prototype user interface. Additionally, proposed Phase II Options 1 and 2 will focus on maturing and optimizing the technology and software, ultimately leading to transition and integration with a targeted program of record.

Benefit:
As military and commercial sensor systems continue to advance, sensor data are being measured and collected at increasing fidelity. High-definition and hyperspectral imagery, full motion video, and synthetic aperture radar and sonar are just a few examples of sensor modalities that produce very high resolution data. Manifold learning exploits the fact that high-dimensional data often lie on intrinsically low-dimensional embedded manifolds. The goal of manifold learning is to uncover the underlying low-dimensional structure and intrinsic characteristics that define the data. Manifold learning provides a means of improving the efficiency and accuracy of high-dimensional data processing by performing data compression and de-noising, which reduces the data sample size required to achieve statistical support. Additionally, manifold learning provides a mechanism for visualizing, characterizing, and understanding complex high-dimensional data. Many techniques exist for performing nonlinear dimensionality reduction; however, existing techniques do not allow a location in the embedded space to be mapped back to the high-dimensional observation space. In other words, new high-dimensional data cannot be synthesized that correspond to locations of interest, possibly unobserved, in the learned low-dimensional manifold. The ability to synthesize new data in the original observed space can be advantageous and even critical for applications that require one of the following: extensive data collection under varying operational conditions, prediction of sequential or temporal data, or data processing or analysis involving a human analyst. Many applications, such as radar combat identification and sonar target recognition for mine countermeasures and anti-submarine warfare, require the collection of significant amounts of data for learning the recognition models. Measured data collection can be a costly exercise, and available data are often limited and not fully representative of target characteristics and environmental conditions that may be encountered in the future. Data collection is often not possible for denied targets and environmental regions. By exploring the low-dimensional embedded space of available data, an analyst can identify critical features for a given objective or features that are not sufficiently sampled by the current data. Generating new high-dimensional data from the current low-dimensional embedding is an efficient and inexpensive way to augment the collected data, resolve critical feature regions on the manifold, and adaptively acquire more relevant data on demand as new environments are encountered. Many data processing applications also require accurate temporal data prediction for successful operation. Dynamic object detection and tracking approaches, such as Kalman filters and particle filters, follow a 2-step process that comprises a signal prediction step and an update step that compares the prediction to the next temporal measurement. Video, radar, and sonar target tracking applications benefit from an accurate predicted estimate of the state or measured signal of an object in the next observation. The intrinsic dynamical processes can be uncovered and modeled in a low-dimensional latent space, with new predicted measurements synthesized in the observation space. Additional applications that benefit from the prediction of observed temporal data include activity recognition, pose estimation, and anomalous behavior detection.

Keywords:
Manifold learning, data synthesis, Nonlinear dimensionality reduction, data visualization, nonparametric Bayesian modeling