arXiv subjects

Liyan Chen

Publications and source records attributed to Liyan Chen.

21 records · Page 2Linked to original sources

arXiv2019

Undirected graphs: is the shift-enabled condition trivial or necessary?

It has recently been shown that, contrary to the wide belief that a shift-enabled condition (necessary for any shift-invariant filter to be representable by a graph shift matrix) can be ignored because any non-shift-enabled matrix can be converted to a shift-enabled matrix, such a conversion in general may not hold for a directed graph with non-symmetric shift matrix. This letter extends this prior work, focusing on undirected graphs where the shift matrix is generally symmetric. We show that while, in this case, the shift matrix can be converted to satisfy the original shift-enabled condition, the converted matrix is not associated with the original graph, that is, it does not capture anymore the structure of the graph signal. We show via a counterexample, that a non-shift-enabled matrix cannot be converted to a shift-enabled one and still maintain the topological structure of the underlying graph, which is necessary to facilitate localized signal processing.

eess.SP↗

arXiv2018

Embedding Multimodal Relational Data for Knowledge Base Completion

Representing entities and relations in an embedding space is a well-studied approach for machine learning on relational data. Existing approaches, however, primarily focus on simple link structure between a finite set of entities, ignoring the variety of data types that are often used in knowledge bases, such as text, images, and numerical values. In this paper, we propose multimodal knowledge base embeddings (MKBE) that use different neural encoders for this variety of observed data, and combine them with existing relational models to learn embeddings of the entities and multimodal data. Further, using these learned embedings and different neural decoders, we introduce a novel multimodal imputation model to generate missing multimodal values, like text and images, from information in the knowledge base. We enrich existing relational datasets to create two novel benchmarks that contain additional information such as textual descriptions and images of the original entities. We demonstrate that our models utilize this additional information effectively to provide more accurate link prediction, achieving state-of-the-art results with a considerable gap of 5-7% over existing methods. Further, we evaluate the quality of our generated multimodal values via a user study. We have release the datasets and the open-source implementation of our models at https://github.com/pouyapez/mkbe

cs.AI↗

arXiv2018

Shift-enabled graphs: Graphs where shift-invariant filters are representable as polynomials of shift operations

In digital signal processing, shift-invariant filters can be represented as a polynomial expansion of a shift operation,that is, the Z-transform representation. When extended to graph signal processing (GSP), this would mean that a shift-invariant graph filter can be represented as a polynomial of the adjacency (shift) matrix of the graph. However, the characteristic and minimum polynomials of the adjacency matrix must be identical for the property to hold. While it has been suggested that this condition might be ignored as it is always possible to find a polynomial transform to represent the original adjacency matrix by another adjacency matrix that satisfies the condition, this letter shows that a filter that is shift invariant in terms of the original graph may not be shift invariant anymore under the modified graph and vice versa. We introduce the notion of "shift-enabled graph" for graphs that satisfy the aforementioned condition, and present a concrete example of a graph that is not "shift-enabled" and a shift-invariant filter that is not a polynomial of the shift operation matrix. The result provides a deeper understanding of shift-invariant filters when applied in GSP and shows that further investigation of shift-enabled graphs is needed to make it applicable to practical scenarios.

eess.SP↗