Decoding the directional focus of an attended speaker from listeners' electroencephalogram (EEG) signals is essential for developing brain-computer interfaces to improve the quality of life for individuals with hearing impairment. Previous works have concentrated on binary directional focus decoding, i.e., determining whether the attended speaker is on the left or right side of the listener. However, a more precise decoding of the exact direction of the attended speaker is necessary for effective speech processing. Additionally, audio spatial information has not been effectively leveraged, resulting in suboptimal decoding results. In this paper, it is found that on the recently presented dataset with 14-class directional focus, models relying exclusively on EEG inputs exhibit significantly lower accuracy when decoding the directional focus in both leave-one-subject-out and leave-one-trial-out scenarios. By integrating audio spatial spectra with EEG features, the decoding accuracy can be effectively improved. The CNN, LSM-CNN, and Deformer models are employed to decode the directional focus from listeners' EEG signals and audio spatial spectra. The proposed Sp-EEG-Deformer model achieves notable 14-class decoding accuracies of 55.35% and 57.19% in leave-one-subject-out and leave-one-trial-out scenarios with a decision window of 1 second, respectively. Experiment results indicate increased decoding accuracy as the number of alternative directions reduces. These findings suggest the efficacy of our proposed dual modal directional focus decoding strategy.

The well-known Gumbel-Max Trick for sampling elements from a categorical distribution (or more generally a non-negative vector) and its variants have been widely used in areas such as machine learning and information retrieval. To sample a random element $i$ in proportion to its positive weight $v_i$, the Gumbel-Max Trick first computes a Gumbel random variable $g_i$ for each positive weight element $i$, and then samples the element $i$ with the largest value of $g_i+\ln v_i$. Recently, applications including similarity estimation and weighted cardinality estimation require to generate $k$ independent Gumbel-Max variables from high dimensional vectors. However, it is computationally expensive for a large $k$ (e.g., hundreds or even thousands) when using the traditional Gumbel-Max Trick. To solve this problem, we propose a novel algorithm, FastGM, which reduces the time complexity from $O(kn^+)$ to $O(k \ln k + n^+)$, where $n^+$ is the number of positive elements in the vector of interest. FastGM stops the procedure of Gumbel random variables computing for many elements, especially for those with small weights. We perform experiments on a variety of real-world datasets and the experimental results demonstrate that FastGM is orders of magnitude faster than state-of-the-art methods without sacrificing accuracy or incurring additional expenses.