The 15 predicted drugs that are known to induce seizures include five are tricyclic antidepressants (TCAs) (amitriptyline, imipramine, nortriptyline, clomipramine, desipramine)
However, our new visualization of the top epilepsy predictions and their targeted genes makes it clear that binding GABAᴬ isn't the cause of these predictions. For convenience, this visualization is reproduced below:
Scooter Morris: Care should be taken against over-interpreting the "clusters" in your visualization. In particular, if you look at the drugs listed closely, you'll see that there are actually two groups with only cyproheptadine and clozapine showing any similarity that crosses the groups. The fact that the two groups are next to each other is a simple artifact of the layout.
Daniel Himmelstein: @scootermorris great point. The 9 ictogenic tricyclic compounds can be broken into two groups based on their structures. First the tricyclic antidepressants — amitriptyline, imipramine, nortriptyline, clomipramine, and desipramine — have the three connected rings with a tail. Second there's cyproheptadine, loxapine, clozapine, and amoxapine, which all have a fourth ring that is not directly touching the tricyclic structure. These four compounds seem to have diverse therapeutic applications: cyproheptadine is a first-generation antihistamine, loxapine is a typical antipsychotic, clozapine is an atypical antipsychotic, and amoxapine is a tetracyclic antidepressant. So @scootermorris I think you're right that the small chemical differences may actual be quite meaningful.
Below is a collection of related literature, which I may update as the research continuous. The primary questions is why the 9 cyclic compounds listed above are ictogenic.
The mechanisms through which antidepressants alter neuronal excitability and modify seizure threshold are still largely unknown. Antidepressants act mainly by blocking the re-uptake of monoamines. Both animal and human data have shown that blocking the re-uptake of norepinephrine and/or serotonin has an anticonvulsant effect . The convulsive properties of antidepressants have been suggested to be the result of their possible local anaesthetic or anticholinergic effect . It has been proposed that selective serotonin re-uptake inhibitors (SSRIs) are less likely to cause seizures than cyclic antidepressants . On the other hand, seizures have been associated with SSRIs in previous studies of adverse events as in the case of escitaloprame .
Antidepressants may disturb the neuronal balance and control of excitability, leading to seizures. Seizures may occur as a consequence of a misbalance between inhibitory GABAergic and excitatory glutamatergic neurotransmission with increase in glutamatergic activation and, thus, excessive calcium influx, initiating intracellular processes. The underlying mechanisms are not clear .
Different specific mechanisms may be involved, which are mediated by the γ-aminobutyric acid (GABA) system and other neurotransmitters. Discussion of these mechanisms is beyond the scope of this review and readers may refer to specific reviews .
From a 1996 article  (referenced in  above):
Taken together, the total body of information strongly suggests that the pharmacodynamic action by which antidepressant drugs cause seizures is unrelated to their ability to block norepinephrine or serotonin reuptake. Rather, it seems more likely that these drugs produce convulsions by virtue of their local anesthetic or their antihistaminic/antimuscarinic properties.
One visually striking pattern is that of the 9 ictogenic tricyclic compounds, 8 target cholinergic receptors. Furthermore, clomipramine also likely exhibits anti-cholinergic effects [1, 2, 3], which would mean all 9 ictogenic tricyclic compounds bind to cholinergic receptors. I have not confirmed this, but I believe these compounds are all antagonists of cholinergic receptors.
There are two anti-ictogenic tricyclic compounds: oxcarbazepine and carbamazepine. Although these compounds likely have anti-cholinergic effects [4, 5, 6], they are unique in their targeting of the sodium channel (according to our visualization).
Interestingly, there's evidence that cholinergic receptor inhibition may a therapeutic mechanism of action for carbamazepine . Quoting from :
The increased sensitivity of these mutant receptors supports the hypothesis that the antiepileptic activity of carbamazepine can, at least to some extent, be attributed to the nAChR inhibition.
And furthermore, the barbiturates — which clustered together and were all anti-ictogenic — also inhibit cholinergic receptors . Pharmacologists believe the primary mechanisms of action for barbituates on epilepsy are GABAᴀ agonism, blocking AMPA/kainate receptors, and inhibiting glutamate release . Potentially, the anti-cholinergic effects of barbiturates are overshadowed by these other mechanisms.