For connection through ssh, you have to specify the ssh user using FTP_USER
define( 'FS_METHOD', 'ssh' );
define( 'FTP_BASE', '/home/user/wordpress' );
define( 'FTP_PUBKEY', '/home/user/.ssh/id_rsa.pub' );
define( 'FTP_PRIKEY', '/home/user/.ssh/id_rsa' );
define( 'FTP_USER', 'user' );
define( 'FTP_HOST', 'localhost:22' );
I think you also need to define FTP_BASE.
You also need to enable ssh upgrade access. From the Codex:
Enabling SSH Upgrade Access
There are two ways to upgrade using SSH2.
The first is to use the SSH SFTP Updater Support plugin. The second is to use the built-in SSH2 upgrader, which requires the pecl SSH2 extension be installed.
To install the pecl SSH2 extension you will need to issue a command similar to the following or talk to your web hosting provider to get this installed:
pecl install ssh2
After installing the pecl ssh2 extension you will need to modify your php configuration to automatically load this extension.
pecl is provided by the pear package in most linux distributions. To install pecl in Redhat/Fedora/CentOS:
yum -y install php-pear
To install pecl in Debian/Ubuntu:
apt-get install php-pear
It is recommended to use a private key that is not pass-phrase protected. There have been numerous reports that pass phrase protected private keys do not work properly. If you decide to try a pass phrase protected private key you will need to enter the pass phrase for the private key as FTP_PASS, or entering it in the “Password” field in the presented credential field when installing updates.