GLMVis

Figure 4.8. A screenshot of the GLMVis interface.

The top row shows the controls — buttons which change the model displayed (in this case relative to different stimuli) or filter the neurons by subject. Below are the parallel coordinate plots, which are separated by brain area (left column ACC, right column dlPFC). Each blue line represents a neuron. Each dotted parallel line represents a dimension that has been fit by the GLM (they correspond to a particular trial condition). The labels on the left group the conditions by color, which correspond to the factor the condition belongs to. For example, the Rule by Rule Repetition interaction is colored green, because Rule @ Repetition1, Rule @ Reptition2, etc. all correspond to the same factor.

A common analysis framework for characterizing the spiking response of neurons is the generalized linear model (GLM) (Fernandes et al., 2014; Harris et al., 2003; Mayo et al., 2015; Park et al., 2014; Pillow, 2005; Truccolo, 2004). GLMs can simultaneously estimate effects of experimental conditions, spike history (refractory period, bursting), non-linear firing rate changes over time, and dependence on other neurons (Truccolo, 2004) — making them useful for analyzing a wide range of experiments. GLMs are especially useful in situations where conditions of interest are interdependent, making them difficult to tease apart using simple tools like peri-event time histograms(MacDonald et al., 2011).

One consequence of being able to estimate many factors simultaneously is that the relationship of the effects becomes hard to understand because of the number of dimensions — particularly if the factors change over time and there are many neurons. Moreover, understanding the relationship between multiple factors may be important to understanding mixed selectivity neurons (Cromer et al., 2010; Fusi et al., 2016; Rigotti et al., 2010). These neurons are sensitive to a combination of sensory, motor and cognitive processes, appear in higher-order association brain regions such as parietal and prefrontal cortex (Park et al., 2014;

Rigotti et al., 2013), and may underlie the computation of complex behavior (Rigotti et al., 2010).

Therefore, we built GLMVis, an interactive visualization for GLMs, that:

(1) shows the relationship between the multiple dimensions of the model fit over time, (2) allows filtering of neurons by effect size, brain area, and experimental

subject, and (3) can be used to compare estimates from different models. To show the relationship between multiple dimensions, we use parallel coordinate plots (Inselberg, 1985; Wegman, 1990) — a compact representation of multivariate data that links each dimension on parallel axes by a line.

Figure 4.8 shows a screenshot of the GLMVis interface. Each axis is a black horizontal line that corresponds to a dimension of the GLM. Non-parallel lines connect the dimensions and represent a single neuron. The intersection of the axes and non-parallel lines is the effect size of the neuron at that dimension.

The user can investigate correlations between dimensions in two ways: clicking on a line, which highlights only that neuron along the dimensions of the model (Figure 4.9c, Figure 4.9d), or by “brushing” along a desired axis — holding and dragging the mouse to filter neurons by effect size in the range of values of the dimension (Figure 4.9a no brushing, Figure 4.9b with brushing). Multiple axes can be “brushed” in order to compare the associations between effects in different dimensions. To further isolate the neurons involved, the user can use dropdown menus to filter the neurons by brain area or experimental subject or compare different models (Figure 4.9d).

Figure 4.9 Interacting with parallel coordinate plots on GLMVis.

(a) Parallel coordinate plot with no brushing. (b) User brushes along the Previous Error – No Previous Error dimension, selecting a group of neurons that co-vary with the Repetition1 – Repetition11+ dimension. (c) User selects a single neuron that varies along the Previous Error – No Previous Error dimension and Repetiton1 – Repetition11+ dimension. (d) User investigates how this model changes with the inclusion of more task factors.

Finally, the user can use GLMVis in conjunction with RasterVis to better understand how the model fits the data. Because parameters can be passed to RasterVis via URL — that is, a URL link can specify the state of RasterVis such as one that corresponds to a dimension of interest for GLMVis — one can easily modify GLMVis such that clicking on a dimension that corresponds to a particular neuron can take the user to that neuron’s raster plot sorted by the dimension of interest. Furthermore, RasterVis can be modified such that the user can make a side-by-side comparison of the actual data and the model-generated

data, allowing for a deeper understanding of the reported effect in conjunction with how well that reported effect captures the structure of the data. This type of deeper understanding between model and data is hard to achieve with static figures, particularly when there is a lot of data and there are many dimensions, because figures for each set of models and data must be generated and then searched for on a file system. Interactivity and the combination of RasterVis and GLMVis allows the user to quickly move back and forth between model and data, gaining insights they might not have otherwise because of the ability to make fast comparisons.

4.5 Discussion

We developed a novel interactive visualization toolkit for investigating

electrophysiological data. This toolkit allows users to quickly explore raw data via RasterVis and intermediate analysis such as receptive fields and networks via GLMVis and SpectraVis. We believe these tools will be important going forward as electrode technology progresses and scientists form more complicated

hypotheses.