Application areas

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We tackle a wide variety of data-driven applications via investigating optimization and machine learning techniques. Here are some exemplified applications, but we do not restrict ourselves to them.

 

Recommendation

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.

An example of color transfer.

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 greatly of 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 network, knowledge graph, 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
Denoising on the COIL20 dataset.

Network traffic analysis (anomaly traffic detection via inverse problem)


Anomaly traffic volume detection by inverse problem.

Wireless system architecture design


Architecture design of hybrid precoder large-scale millimeter wave (mmWave) MIMO systems.

General-purpose data analysis

Principal component analysis (PCA).