that could be good bases for your class, I guess:
class MyClass {
    // you may need to set the proper types in accordance with your dictionarty's content
    var title: String?
    var shortDescription: String?
    var newsDescription: String?
    var link: NSURL?
    var pubDate: NSDate?
    //
    init () {
        // uncomment this line if your class has been inherited from any other class
        //super.init()
    }
    //
    convenience init(_ dictionary: Dictionary<String, AnyObject>) {
        self.init()
        title = dictionary["title"] as? NSString
        shortDescription = dictionary["shortDescription"] as? NSString
        newsDescription = dictionary["newsDescription"] as? NSString
        link = dictionary["link"] as? NSURL
        pubDate = self.getDate(dictionary["pubDate"])
    }
    //
    func getDate(object: AnyObject?) -> NSDate? {
        // parse the object as a date here and replace the next line for your wish...
        return object as? NSDate
    }
}
advanced-mode
I would like to avoid to copy-pand-paste the keys in a project, so I'd put the possible keys into e.g. an enum like this:
enum MyKeys : Int {
    case KeyTitle, KeyShortDescription, KeyNewsDescription, KeyLink, KeyPubDate
    func toKey() -> String! {
        switch self {
        case .KeyLink:
            return "title"
        case .KeyNewsDescription:
            return "newsDescription"
        case .KeyPubDate:
            return "pubDate"
        case .KeyShortDescription:
            return "shortDescription"
        case .KeyTitle:
            return "title"
        default:
            return ""
        }
    }
}
and you can improve your convenience init(...) method like e.g. this, and in the future you can avoid any possible mistyping of the keys in your code:
convenience init(_ dictionary: Dictionary<String, AnyObject>) {
    self.init()
    title = dictionary[MyKeys.KeyTitle.toKey()] as? NSString
    shortDescription = dictionary[MyKeys.KeyShortDescription.toKey()] as? NSString
    newsDescription = dictionary[MyKeys.KeyNewsDescription.toKey()] as? NSString
    link = dictionary[MyKeys.KeyLink.toKey()] as? NSURL
    pubDate = self.getDate(dictionary[MyKeys.KeyPubDate.toKey()])
}
NOTE: that is just a raw idea of how you could do it, it is not necessary to use conveniece initializer at all, but it looked obvious choice regarding I don't know anything about your final class – you have shared one method only.