Information-theoretic metric learning: 2-D linear projections of neural data for visualization

Abstract

Abstract-Intracortical neural recordings are typically highdimensional due to many electrodes, channels, or units and high sampling rates, making it very difficult to visually inspect differences among responses to various conditions. By representing the neural response in a low-dimensional space, a researcher can visually evaluate the amount of information the response carries about the conditions. We consider a linear projection to 2-D space that also parametrizes a metric between neural responses. The projection, and corresponding metric, should preserve class-relevant information pertaining to different behavior or stimuli. We find the projection as a solution to the information-theoretic optimization problem of maximizing the information between the projected data and the class labels. The method is applied to two datasets using different types of neural responses: motor cortex neuronal firing rates of a macaque during a center-out reaching task, and local field potentials in the somatosensory cortex of a rat during tactile stimulation of the forepaw. In both cases, projected data points preserve the natural topology of targets or peripheral touch sites. Using the learned metric on the neural responses increases the nearest-neighbor classification rate versus the original data; thus, the metric is tuned to distinguish among the conditions.

Learning multiscale neural metrics via entropy minimization

“…The classification results are tabulated in Table II, with a negligible increase of the classification rate versus the binned approach. V. CONCLUSION We presented an approach to learn weighted combinations of metrics or kernels for neural response classification, extending previous work [4]. The metric-learning hinges on a kernel matrix-based measure of entropy [3], [8].…”

“…From this a measure of conditional entropy S α (B|C) = S α (B, C) − S α (C) can be applied, and this form of conditional entropy was used in previous work for learning a Mahalanobis distance [3], [4].…”

“…As opposed to previous work [4], we avoid using linear projections, instead learning new metrics/kernels as the combination metrics/kernels for different dimensions of the neural response. This enables us to learn multiscale measures such as combinations of spike-train metrics or weighted combinations of kernels with different kernel sizes.…”

Decoding methods for neural prostheses: where have we reached?

“…Several other methods have been used in the recent literature: kernel autoregressive moving average (KARMA; Wong et al, 2013), quantized kernel least mean square (Li et al, 2014), support vector machines (Cao et al, 2013; Xu et al, 2013; Wang et al, 2014), K-nearest neighbors (Brockmeier et al, 2013; Ifft et al, 2013; Xu et al, 2013), naïve Bayes (Bishop et al, 2014), and artificial neural networks (Chen et al, 2013; Mahmoudi et al, 2013; Pohlmeyer et al, 2014). All of these methods allow highly non-linear neural models.…”

“…Also using a supervised approach, Brockmeier et al (2013) proposed a method for computing a linear dimensionality reduction which maximizes the information between the class labels and the projected neural data. The low dimensional data can be used for visualization or decoding via distance-based methods such as K-nearest neighbors.…”