Related papers: Enumerative Encoding in the Grassmannian Space
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
Representation Learning of words and Knowledge Graphs (KG) into low dimensional vector spaces along with its applications to many real-world scenarios have recently gained momentum. In order to make use of multiple KG embeddings for…
Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional sub- space structures embedded in data. One of its successful applications is subspace clustering, by which data…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale…
There has been a surge of recent interest in learning representations for graph-structured data. Graph representation learning methods have generally fallen into three main categories, based on the availability of labeled data. The first,…
The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an…
A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation…
Visual observations of dynamic phenomena, such as human actions, are often represented as sequences of smoothly-varying features . In cases where the feature spaces can be structured as Riemannian manifolds, the corresponding…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
For every linear binary code $C$, we construct a geometric triangular configuration $\Delta$ so that the weight enumerator of $C$ is obtained by a simple formula from the weight enumerator of the cycle space of $\Delta$. The triangular…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges. This class includes three prominent members: conventional arithmetic coding, range…
Many computer vision algorithms employ subspace models to represent data. The Low-rank representation (LRR) has been successfully applied in subspace clustering for which data are clustered according to their subspace structures. The…
Vector representations of words have heralded a transformational approach to classical problems in NLP; the most popular example is word2vec. However, a single vector does not suffice to model the polysemous nature of many (frequent) words,…
Fibonacci codes are self-synchronizing variable-length codes that are proven useful for their robustness and compression capability. Asymptotically, these codes provide better compression efficiency as the order of the underlying Fibonacci…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
Graphcodes were recently introduced as a technique to employ two-parameter persistence modules in machine learning tasks (Kerber and Russold, NeurIPS 2024). We show in this work that a compressed version of graphcodes yields a description…
Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a…
With Grassmann algebra as fermions in a Feynman path-integral approach to field theory, the quantum correlation can be recovered. This means that a quantum field of Grassmann variables can explain the entanglement. In turn, this agrees with…