PIP Distance: A Unitary-invariant Metric for Understanding Functionality and Dimensionality of Vector Embeddings.
Zi YinPublished in: CoRR (2018)
Keyphrases
- distance measure
- vector space
- distance function
- euclidean distance
- dimensionality reduction
- intrinsic dimension
- cosine distance
- distance metric
- intrinsic dimensionality
- high dimensional
- low dimensional
- spatial distance
- metric space
- euclidean space
- euclidean metric
- triangle inequality
- invariant features
- feature space
- hausdorff distance
- neural network
- moment invariants
- distance matrix
- triangular inequality
- manhattan distance
- similarity metric
- affine invariant
- information content
- manifold learning
- high dimensional data
- feature vectors
- similarity measure
- data sets
- geodesic distance
- deeper understanding
- mahalanobis distance
- spatial distribution
- metric learning
- vector data
- sparse matrix
- invariant properties