Linear Tensor Projection Revealing Nonlinearity
This work addresses the challenge of interpreting complex, nonlinear decision boundaries in high-dimensional data for users in fields like data analysis, though it appears incremental as it builds on existing dimensionality reduction techniques.
The paper tackles the problem of linear dimensionality reduction methods failing to capture important nonlinear correlations for prediction, especially with matrix or tensor data, by proposing a method that finds a subspace maximizing prediction accuracy while preserving data information, and demonstrates its effectiveness on various data types.
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component analysis and linear discriminant analysis, make it possible to capture the correlation between many variables; however, there is no guarantee that the correlations that are important in predicting data can be captured. Moreover, if the decision boundary has strong nonlinearity, the guarantee becomes increasingly difficult. This problem is exacerbated when the data are matrices or tensors that represent relationships between variables. We propose a learning method that searches for a subspace that maximizes the prediction accuracy while retaining as much of the original data information as possible, even if the prediction model in the subspace has strong nonlinearity. This makes it easier to interpret the mechanism of the group of variables behind the prediction problem that the user wants to know. We show the effectiveness of our method by applying it to various types of data including matrices and tensors.