Decoding PRR Responses

Previous studies have decoded the responses of PRR neurons to reaches made in the frontoparallel plane with central fixation (Shenoy, Meeker et al. 2003; Musallam, Corneil et al. 2004). The sophisticated decode methods employed in these studies transformed planning period responses using wavelets, and built databases of these responses during the initial portion of each experimental session for online decoding using a Bayesian framework. Studies by Gail et al. and Quian-Quiroga et al. have applied nearest neighbor methods for decoding planning period activity in PRR neurons (Gail and Andersen 2006; Quian Quiroga, Snyder et al. 2006). These methods do not transform spiking responses, and instead use firing rates averaged across the entire memory period, or firing rates over trial time (estimated from PSTHs). Again, a database of trials are used as a training set, and the relevant parameters are decoded from test trials by obtaining the class of the training trial firing rate nearest (by Euclidean distance) to the test trial firing rate. The nearest neighbor method is easily implemented, however does not take into account the variability in the firing rate in the relation to the classes of data during which linear discriminant analysis does by classifying data based on within-class and between-class variance (Bishop 1995; Hastie, Tibshirani et al. 2001).

In this work, we have performed some preliminary decode analyses on decoding reach target disparity, fixation depth, and absolute depth from the decoupled reach target experiment (Experiment 2). We have employed both nearest neighbor and linear discriminant decodes, as they yield different results. Figure 4-33 illustrates a neuron dropping curve using the nearest neighbor decode on reach target depth when the monkey

fixated at 13° of vergence angle. (Neuron dropping curves at other vergence angles are nearly identical, not shown.) Cross validation was performed on 100 sets of randomly selected neurons (without replacement) for each number of neurons used in the decode analysis, and the mean and standard deviation of performance is shown on the plot. Chance level performance is 20%, and is exceeded reliably (lower bound of performance using one standard deviation) with as little as 10 neurons. As documented in numerous studies, decode performance follows a near log function with the number of neurons.

Decode performance for both reach target disparity and fixation depth over trial time is shown in Figure 4-34. Reach target disparity is decoded using all fixation depths.

Decode performance for reach target disparity rises significantly above chance level once the cue is flashed as expected (vertical line shows cue offset/memory begin). Decode performance dips slightly (~5% averaged across the memory period decode compared to

Figure 4-33 Neuron dropping curve using the nearest neighbor decode., plotting the average decode performance for reach target disparity at 13° of vergence angle against the number of neurons. Error bars indicate standard deviation from 100 cross validation sets, where neurons were selected at random without replacement.

the peak decode performance during cue presentation) during the planning period,

however remains well above chance performance. The decode performance for vergence angle remains constant across trial time, as expected since vergence angle is maintained. Other parameters in the nearest neighbor decode were employed – it is possible to use the n nearest neighbors to determine the task condition, however using n = 2,… 7 did not yield significant performance improvements. In addition, other distance measures can be used – interestingly, city block distance yielded some improvements in decode

performance (~5%) when all neurons are used in the decode (performance difference decreases with fewer neurons), and indicate that the distance measure has a measurable dependence on when the dimensionality of the input vector becomes large (number of neurons in the population).

Figure 4-34 Decode

performance using the nearest neighbor decode across trial time using all neurons. All conditions in Experiment 2 were included, and reach target depth and vergence angle were

separately decoded. Chance levels are indicated by the dotted lines.

As a comparison, Figure 4-35shows the decode performance across trial time using the linear discriminant. The same parameters for obtaining the firing rate from trials and cross validation are used. A diagonal covariance matrix was used since enough training

trials were not available for estimating a pooled covariance matrix with the total population of neurons. A large increase in decode performance is realized with this method, and shows that the use of class variability in the decode is an important factor. The same trend over trial time for decode performance exists between decode methods – vergence angle decode performance remains constant, and reach target disparity

decodability rises with the presentation of the cue and persists through the planning period. There is a marked difference in decode performance between the methods in the motor period (the reach occurs approximately 1400 – 1600ms after cue offset); a peak is observed using LDA which is absent in the nearest neighbor method, again indicating that accounting for response variability between classes is an important feature in decoding firing rates in this task. Lastly, the combination of reach target disparity and vergence angle, which indicates the absolute depth of the target in eye centered

coordinates, is decoded (black trace). Though chance level for decoding both parameters

Figure 4-35 Decode performance using linear discriminant analysis across trial time using all neurons. All conditions in Experiment 2 were included and decoded; reach target depth (reach), vergence angle(fix), and the combination of reach target depth and vergence angle (all).

is 5% (1/20; vs. 20%, 1/5 for disparity and 25%, 1/4 for vergence angle), the performance nearly tracks the decode of disparity alone. The results illustrate that the activity of population of PRR neurons can be used to decode the absolute depth or a reach target during movement planning.

Chapter 5

Discussion