Signals and Data Analysis

In our world, data is collected on just about everything. Researchers are interested in determining ways to glean information from this data. They might want to find patterns in the data that are unique to a particular scenario. How often does the apparent luminosity of a distant star fall because of the transit of an orbiting planet? When is the best time to advertise your product to users on a social media platform? How do we determine climate change patterns? Researchers are also interested in how to determine what the data tells them about grouping like subjects in their study. Which advertisement type matches with which social media behavior? How can we classify animal fossils to link extinct animals to the animals we see around us? Scientists are interested in determining the division between unlike subjects. Will a particular demographic vote for a particular candidate based on key features in an ad campaign? They might want to predict outcomes based on data already collected. What can downstream flow and turbidity data reveal about forest health and snow pack in the upstream mountains? Image analysts are interested in recovering images, determining image similarity, and manipulating images and videos. How can we recover the 3D structure of an object from many 2D pictures? How can we view brain features from CAT scans using fewer scans? How do we create smooth transitions between images in a video?

Machine learning is an active area of data analysis research. The overarching goal of machine learning is to create mathematical tools that instruct computers on classification of research subjects or how to predict outcomes. Some key tools of machine learning are Fourier analysis (for pattern recognition), regression analysis (for predictions), support vector machines (for classification), and principle component analysis (for finding relevant features or structure).