Wikipedia
Vinayaki is an elephant-headed Hindu goddess. Her mythology and iconography are not clearly defined. Little is told about her in Hindu scriptures and very few images of this deity exist.
Due to her elephantine features, the goddess is generally associated with the elephant-headed god of wisdom, Ganesha. She does not have a consistent name and is known by various names, Stri Ganesha ("female Ganesha"), Vainayaki, Gajananā ("elephant-faced"), Vighneshvari ("Mistress of obstacles") and Ganeshani, all of them being feminine forms of Ganesha's epithets Vinayaka, Gajanana, Vigheshvara and Ganesha itself. These identifications have resulted in her being assumed as the shakti - feminine form of Ganesha.
Vinayaki is sometimes also seen as the part of the sixty-four yoginis or the matrika goddesses. However, scholar Krishan believes that Vinayakis in early elephant-headed matrikas, the Brahmnaical shakti of Ganesha, and the Tantric yogini are three distinct goddesses.
In the Jain and Buddhist traditions, Vinayaki is an independent goddess. In Buddhist works, she is called Ganapatihridaya ("heart of Ganesha").