Wordsworth’s Negative Way

Multi-way Clustering Using Super-Symmetric Non-negative Tensor Factorization

We consider the problem of clustering data into k ≥ 2 clusters given complex relations — going beyond pairwise — between the data points. The complex n-wise relations are modeled by an n-way array where each entry corresponds to an affinity measure over an ntuple of data points. We show that a probabilistic assignment of data points to clusters is equivalent, under mild conditional independence...

Wiener Way to Dimensionality

This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the t...

On Parmenides' Poem: "The Way of Truth" and "The Way of Opinion"

Low-rank Approximation Based non-Negative Multi-Way Array Decomposition on Event-Related potentials

Non-negative tensor factorization (NTF) has been successfully applied to analyze event-related potentials (ERPs), and shown superiority in terms of capturing multi-domain features. However, the time-frequency representation of ERPs by higher-order tensors are usually large-scale, which prevents the popularity of most tensor factorization algorithms. To overcome this issue, we introduce a non-ne...

Non-negative Matrix Factorization: A possible way to learn sound dictionaries

Auditory system detects sound signals and uses the temporal-frequency information of the sound signals to conduct sound identification, sound localization, and sound source separation. Thanks to the past studies, we know that the hair cells at cochlea show frequency-dependent responses against input sound signals. But, little is known about how the sound information is conducted to and processe...