Challenges in designing subspace learning can be expressed in terms of challenges met in the observed data and in terms of challenges that should tackle algorithms in the concerned applications.
Challenges in the observed data (Details)
Presence of Outliers or Missing Data. [Robustness]
Number of Outliers or Missing Data. [Robustness]
Distribution of Outliers or Missing Data. [Gaussian, Laplacian]
High dimensional data. [Sparsity]
Large-scale Dataset. [Distributed] [Scalability]
Euclidean Structure/Geometry Structure.
Out-of-sample Problem.
Small-sample-size problem.
Challenges for algorithms (Details)
Provably correct and under what assumptions?
Practical accuracy.
Time complexity.
Memory complexity and/or number of passes.
Incremental versus batch.
Online versus offline.
Sequential versus parallel.
Streaming and nearly-streaming
Real-time or not.