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I am new to neural networks. Is it possible to train a neural network to identify only one type of object? For instance, a table from a large set of images, where the neural network should be able to identify if new images are tables.

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Yes, you can train a NN to detect only one type of object like a table. However, you probably will not want to train such a NN from scratch by showing some examples of tables and non-tables. You will need to use transfer learning on a model already trained on several image classes and teach it to also recognize your new class. This transfer learning requires a smaller set of desired images. You may need to give it some negative examples also. You should explore transfer learning with mobilenet, inception, and other pre-trained Tensorflow models if you are willing to use Python and Tensorflow

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