Application areas
We tackle a wide variety of data-driven applications by investigating optimization and machine-learning techniques. Here are some exemplified applications, but we do not restrict ourselves to them.
Recommendation
The low-rank approximation has attracted more and more attention in the community of recommendation. A fundamental assumption in constructing matrix approximations is that the partially observed data matrix is of low rank. A matrix completion (imputation) gives a tool to predict missing entries for a recommendation system.
Movie recommendation by matrix completion problem.
Color transfer
Color transfer is a method of transferring color information from a source image to a target image by considering a reference image. This problem is presented in terms of the optimal transportation problem.
Classification, matching, and clustering of sequential data
Text, video sequence, speech, DNA, financial transactions, stock prices, customer action histories, human actions, and human behavioral histories are sequential data. Classification, matching, and clustering of such sequential data are of great importance in data analysis in theory as well as in practice. Many of them are defined as optimization problems.
An example of sequence matching between two time-series data of human actions.
Classification, matching, and clustering of graph-structured data
Many real-world data such as social networks, chemical molecules, citation networks, knowledge graphs, or image data are represented in graph-structured data. Classification, matching, and clustering of such graph-structured data are important fundamental problems in data analysis. Many of them are formulated as optimization problems.
Examples of graph matching between two graph-structured data.
Video surveillance (anomaly detection)
Video sequence understanding by online subspace learning with matrix and tensor representations.
Image processing (recovery, basis representation, and denoising)
Hyperspectral image recovery on the Ribeira dataset
Network traffic analysis (anomaly traffic detection via inverse problem)
Anomaly traffic volume detection by the inverse problem.
Wireless system architecture design
Architecture design of hybrid precoder large-scale millimeter wave (mmWave) MIMO systems.
General-purpose data analysis
