wpquestions.com, ID = 2880

// set nav item classes to an empty array
function filter_nav_menu_classes( $classes ) {

    // create array for new classes
    $new_classes = array();

    // return the new array with classes
    return $new_classes;

}

add_filter( 'nav_menu_css_class', 'filter_nav_menu_classes' );


// custom walker for the nav menu
class clean_html_walker extends Walker_Nav_Menu
{
    function start_el(&$output, $item, $depth, $args) {
        global $wp_query;
        $indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';

        $class_names = $value = '';

        $classes = empty( $item->classes ) ? array() : (array) $item->classes;
        $classes[] = 'menu-item-' . $item->ID;

        $class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item, $args ) );
        $class_names = !empty( $class_names ) ? ' class="' . esc_attr( $class_names ) . '"' : '' ; // print out the attribute if the array with classes is not empty

        $id = apply_filters( 'nav_menu_item_id', 'menu-item-'. $item->ID, $item, $args );
        $id = strlen( $id ) ? ' id="' . esc_attr( $id ) . '"' : '';

        $output .= $indent . '<li' . $id . $value . $class_names .'>';

        $attributes  = ! empty( $item->attr_title ) ? ' title="'  . esc_attr( $item->attr_title ) .'"' : '';
        $attributes .= ! empty( $item->target )     ? ' target="' . esc_attr( $item->target     ) .'"' : '';
        $attributes .= ! empty( $item->xfn )        ? ' rel="'    . esc_attr( $item->xfn        ) .'"' : '';
        $attributes .= ! empty( $item->url )        ? ' href="'   . esc_attr( $item->url        ) .'"' : '';

        $item_output = $args->before;
        $item_output .= '<a'. $attributes .'>';
        $item_output .= $args->link_before . apply_filters( 'the_title', $item->title, $item->ID ) . $args->link_after;
        $item_output .= '</a>';
        $item_output .= $args->after;

        $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
    }
}