  This paper proposes a novel method of independent component analysis (ICA),
which we name higher-order tensor ICA (HOT-ICA). HOT-ICA is a tensor ICA that
makes effective use of the signal categories represented by the axes of a
separating tensor. Conventional tensor ICAs, such as multilinear ICA (MICA)
based on Tucker decomposition, do not fully utilize the high dimensionality of
tensors because the matricization in MICA nullifies the tensor axial
categorization. In this paper, we deal with multiple-target signal separation
in a multiple-input multiple-output (MIMO) radar system to detect respiration
and heartbeat. HOT-ICA realizes high robustness in learning by incorporating
path information, i.e., the physical-measurement categories on which
transmitting/receiving antennas were used. In numerical-physical experiments,
our HOT-ICA system effectively separate the bio-signals successfully even in an
obstacle-affecting environment, which is usually a difficult task. The results
demonstrate the significance of the HOT-ICA, which keeps the tensor
categorization unchanged for full utilization of the high-dimensionality of the
separation tensor.
