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Mathematical Sciences

Research project: Optimisation in Data Dimension Reduction and Visualization

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The fundamental problem of dimensionality reduction arises from analysing and visualizing very high dimensional data. Fast optimization methods are becoming an indispensable tool in deriving high-quality low-dimensional embedding. Our research focuses on distance embedding methods, especially for large scale data that is incomplete or has missing values.  Applications include sensor network localization, classification of high-dimensional images and visualizing social networks.

 Optimisation in Data Analysis
Sensor network localization

Sensor network localization

In sensor network localization, due to the range limitation of sensors, the collected distance information often is inaccurate and incomplete. The task is to find the localization of those sensors based on the obtained range information. This leads to optimal matrix completion and approximation in large scale.

Classifying high-dimensional images

Classifying high-dimensional images

In classifying high-dimensional images, the distinction between images only depends on a few variables such as pose, light, and angle. Therefore, low-dimensional representation of those images are possible. The purpose is to find the best low-dimensional representation that is likely to yield the best classification.

Social networks

Social networks

In social networks, dissimilarity data often incomplete can be cheaply collected and it is dynamic. Fast visualization methods are essential in real-time analysis of such networks. Optimization of certain quantity of interest often leads to high-quality visualization that reveals hidden structures of the network.

Related research groups

Operational Research
Computational Optimisation
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