tIFFS: an approach to define a theoretically infinite family of feature space for an artificial intelligence framework

In the current artificial intelligence (AI) framework, the explainability of AI is buried under the black-box nature of the implicit implementation of the latent feature space of an AI architecture. However, the explainability of AI can be enhanced by explicitly defining its feature space, quantifying the similarity (or dissimilarity) and orthogonality (or non-orthogonality) properties between its feature vectors, and extracting common features (projection onto subspaces) of its feature vectors. Hence, this paper presents an approach that defines a theoretically infinite family of features space (tIFFS) that uniquely combines the distinctive properties of inner product and orthogonality operations between feature vectors, and the projection of feature vectors onto subspaces in a Hilbert space. The tIFFS approach utilizes the concept of “infinite mixture model” of the (i) Bayesian Gaussian mixture model (also called the Dirichlet Process mixture model (DPMM)), (ii) spectral density of the DPMM output in the Fourier domain, and (iii) Hilbert space that is formed by infinite dimension function space (IDFS). The phase information that carries the orthogonality, orientation, and gradient features of the DPMM output in the Fourier domain is also utilized to precisely define subspace boundaries and capture similarity and dissimilarity features of the feature vectors. In addition, the tIFFS approach adapts principal component analysis to integrate the well-defined orthogonality properties of eigenvectors and eigenvalues of the covariance matrix of the feature vectors in Hilbert space. A simulation is conducted to develop random forest (RF) classifiers to classify backyard birds using tIFFS. The simulation with images of 147 Northern Cardinals, 147 American Robin, and 147 House Finches show the RF-classifiers that achieve the precision-score of about 88% and F1-score of about 86% can be developed by fine tuning the model and eigenvector (or eigenvalue) parameters. Hence, it shows that the tIFFS can capture suitable inner product, orthogonality, and projection properties in the IDFS Hilbert space.