We present a morphological classification of 14,245 radio active galactic nuclei (AGNs) into six types, i.e., typical Fanaroff--Riley Class I / II (FRI/II), FRI/II-like bent-tailed, X-shaped radio galaxy, and ringlike radio galaxy, by designing a convolutional neural network (CNN) based autoencoder, namely MCRGNet, and applying it to a labeled radio galaxy (LRG) sample containing 1442 AGNs and an unlabeled radio galaxy (unLRG) sample containing 14,245 unlabeled AGNs selected from the Best--Heckman sample. We train MCRGNet and implement the classification task by a three-step strategy, i.e., pre-training, fine-tuning, and classification, which combines both unsupervised and supervised learnings. A four-layer dichotomous tree is designed to classify the radio AGNs, which leads to a significantly better performance than the direct six-type classification. On the LRG sample, our MCRGNet achieves a total precision of $sim 93%$ and an averaged sensitivity of $sim 87%$, which are better than those obtained in previous works. On the unLRG sample, whose labels have been human-inspected, the neural network achieves a total precision of $sim 80%$. Also, using the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) to calculate the $r$-band absolute magnitude ($M_mathrm{opt}$) and using the flux densities to calculate the radio luminosity ($L_mathrm{radio}$), we find that the distributions of the unLRG sources on the $L_mathrm{radio}$--$M_mathrm{opt}$ plane do not show an apparent redshift evolution and could confirm with a sufficiently large sample that there could not exist an abrupt separation between FRIs and FRIIs as reported in some previous works.
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