3 research outputs found
Directional clustering through matrix factorization
This paper deals with a clustering problem where feature vectors are clustered depending on the angle between feature vectors, that is, feature vectors are grouped together if they point roughly in the same direction. This directional distance measure arises in several applications, including document classification and human brain imaging. Using ideas from the field of constrained low-rank matrix factorization and sparse approximation, a novel approach is presented that differs from classical clustering methods, such as seminonnegative matrix factorization, K-EVD, or k-means clustering, yet combines some aspects of all these. As in nonnegative matrix factorization and K-EVD, the matrix decomposition is iteratively refined to optimize a data fidelity term; however, no positivity constraint is enforced directly nor do we need to explicitly compute eigenvectors. As in k-means and K-EVD, each optimization step is followed by a hard cluster assignment. This leads to an efficient algorithm that is shown here to outperform common competitors in terms of clustering performance and/or computation speed. In addition to a detailed theoretical analysis of some of the algorithm's main properties, the approach is empirically evaluated on a range of toy problems, several standard text clustering data sets, and a high-dimensional problem in brain imaging, where functional magnetic resonance imaging data are used to partition the human cerebral cortex into distinct functional regions
Neural System Identification with Spike-triggered Non-negative Matrix Factorization
Neuronal circuits formed in the brain are complex with intricate connection
patterns. Such complexity is also observed in the retina as a relatively simple
neuronal circuit. A retinal ganglion cell receives excitatory inputs from
neurons in previous layers as driving forces to fire spikes. Analytical methods
are required that can decipher these components in a systematic manner.
Recently a method termed spike-triggered non-negative matrix factorization
(STNMF) has been proposed for this purpose. In this study, we extend the scope
of the STNMF method. By using the retinal ganglion cell as a model system, we
show that STNMF can detect various computational properties of upstream bipolar
cells, including spatial receptive field, temporal filter, and transfer
nonlinearity. In addition, we recover synaptic connection strengths from the
weight matrix of STNMF. Furthermore, we show that STNMF can separate spikes of
a ganglion cell into a few subsets of spikes where each subset is contributed
by one presynaptic bipolar cell. Taken together, these results corroborate that
STNMF is a useful method for deciphering the structure of neuronal circuits.Comment: updated versio
Directional Clustering through Matrix Factorization Experiments
These data files and matlab scripts allow the user to recreate the numerical experiments in the paper Thomas Blumensath, "Directional Clustering through Matrix Factorisation," to appear in IEEE Transactions on Neural Networks and Learning Systems.Funded by EPSRC (EP/J005444/1; Advanced FMRI acquisition, reconstruction and signal processing for dynamic brain network imaging; 2012 to 2015).</span