Basically just the header.
The question is out of curiosity as I haven't seen one yet.
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3$\begingroup$ You could always split the complex number into two, the real and complex part, so 2 columns and use a regular ML model, if this makes sense. $\endgroup$– user2974951Oct 22, 2021 at 7:39
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$\begingroup$ Never heard of any, it's hard to imagine an application of ML where that would make sense. $\endgroup$– ErwanOct 22, 2021 at 16:10
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$\begingroup$ @user2974951 I get what you mean, but I'm more interested in how complex numbers could be useful at all, not in how it's implemented. $\endgroup$– Moritz GroßOct 22, 2021 at 18:16
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$\begingroup$ I'm not an expert, but the positional encoding in the Attention is all you need paper, on which Bert and other popular modern models seem to be based, looks like a Fourier transform of the position to me. So you could probably say these popular models use complex numbers. $\endgroup$– ValentasOct 22, 2021 at 18:21
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1$\begingroup$ Fourier transform of a time series? (I have a post on the imaginary components of Fourier transforms that some of you might be interested in reading.) $\endgroup$– DaveOct 22, 2021 at 18:22
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1 Answer
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As it turns out there are Neural Networks which are designed to work with complex numbers:
A Survey of Complex-Valued Neural Networks
Artificial neural networks (ANNs) based machine learning models and especially deep learning models have been widely applied in computer vision, signal processing, wireless communications, and many other domains, where complex numbers occur either naturally or by design. However, most of the current implementations of ANNs and machine learning frameworks are using real numbers rather than complex numbers. There are growing interests in building ANNs using complex numbers, and exploring the potential advantages of the so-called complex-valued neural networks (CVNNs) over their real-valued counterparts. In this paper, we discuss the recent development of CVNNs by performing a survey of the works on CVNNs in the literature. Specifically, a detailed review of various CVNNs in terms of activation function, learning and optimization, input and output representations, and their applications in tasks such as signal processing and computer vision are provided, followed by a discussion on some pertinent challenges and future research directions.
There are also complex-valued SVMs:
Complex and Hypercomplex-Valued Support Vector Machines: A Survey
In recent years, the field of complex, hypercomplex-valued and geometric Support Vector Machines (SVM) has undergone immense progress due to the compatibility of complex and hypercomplex number representations with analytic signals, as well as the power of description that geometric entities provide to object descriptors. Thus, several interesting applications can be developed using these types of data and algorithms, such as signal processing, pattern recognition, classification of electromagnetic signals, light, sonic/ultrasonic and quantum waves, chaos in the complex domain, phase and phase-sensitive signal processing and nonlinear filtering, frequency, time-frequency and spatiotemporal domain processing, quantum computation, robotics, control, time series prediction, and visual servoing, among others. This paper presents and discusses the importance, recent progress, prospective applications, and future directions of complex, hypercomplex-valued and geometric Support Vector Machines.
