Installing MySQL without root access

I am trying to install MySQL without root permissions. I ran through the following steps:

1. Download MySQL Community Server 5.5.8 Linux - Generic Compressed TAR Archive
2. Unpack it, for example to: /home/martin/mysql

3. Create a my.cnf file in your home directory. The file contents should be:

   [server]
   user=martin
   basedir=/home/martin/mysql
   datadir=/home/martin/sql_data
   socket=/home/martin/socket
   port=3666
   

4. Go to the /home/martin/mysql directory and execute:

   ./scripts/mysql_install_db --defaults-file=~/my.cnf --user=martin --basedir=/home/martin/mysql --datadir=/home/martin/sql_data --socket=/home/martin/socket
   

5. Your MySQL server is ready. Start it with this command:

   ./bin/mysqld_safe --defaults-file=~/my.cnf &
   

When I try to change the password of MySQL it gives the error:

Cannot connect to mysql server through socket '/tmp/mysql.sock'

How can I change this path and see whether the mysql.sock is created or not?

change the socket=/home/martin/socket to /tmp/mysql.sock