The Power of Linear Algebra in Interpreting Space Data
The challenge of space data redundancy and how to solve it.
The vastness of our universe mirrors the overwhelming amount of data we gather from our space observatories and satellites. For instance, the Hubble Telescope alone has produced data equivalent to 75 million e-books. Moreover, once the SKA is up and running at full capacity, we are looking at several petabytes of data daily. With these figures in mind, how can data scientists effectively sift through this mountain of information? I believe that linear algebra is not just a mere mathematical tool but a practical means to develop algorithms that find patterns in space.
The Practicality of Singular Value Decomposition (SVD)
One of the immediate challenges with the data from space observatories is redundancy. Why? Space observatories often observe the same regions of space multiple times to improve the signal-to-noise ratio. So, repeated observation can lead to a significant amount of duplicated information in the datasets.
Singular Value Decomposition (SVD) is a linchpin of linear algebra, it offers a sophisticated method to breakdown complex matrices into key components: two orthogonal matrices, and a diagonal matrix, which consists of singular values. Typically, only a handful of these singular values (often the largest ones) capture the majority of the variance in the data. So, if we retain only the components associated with these dominant singular values, we can represent the image with fewer data points, reducing redundant or less significant information.
Once the noise is reduced and essential patterns are emphasised, advanced algorithms can take over, deep diving into these patterns, potentially recognising nuances that might otherwise have been missed. For instance, detecting a previously unobserved star formation sequence or identifying anomalies in the movement of celestial bodies becomes more feasible.
Pattern Recognition with Eigenvalues and Eigenvectors
If we dive into the foundational principles that empower these algorithms, we must mention two basic principles of linear algebra: eigenvalues and eigenvectors. They have practical applications, especially in the field of astronomy. More specifically, when observing celestial movements, eigenvectors can depict the consistent patterns or trends inherent in these motions, whilst eigenvalues give us a measure of how important or influential these patterns are. By harnessing these linear algebra tools, we can highlight some hidden astronomical events and details, turning them from barely noticeable to clearly observable.
Conclusion
As our observatories and satellites continue to produce vast amounts of space data, the challenge is not just about storage or volume, it is also about techniques enabling better interpretation. Luckily, linear algebra offers clear and practical tools to explore this data effectively. As a result, SVD as well as eigenvalue and eigenvectors can help data scientists identify and understand unseen patterns of the universe. They not merely mathematical approaches; they are vital strategies for improving our understanding of space data.