Imagine it is mosaic mosaic mosaic .... n times ... mosaic of datasets and that tree of those mosaic/datasets it is just one of the possible interpretations of the main dataset send by the aliens. The same way as you may have an encrypted message, which is compiled in the way that there exists set of m keys with decodes the encrypted message in m meaningful texts.
Each time you decode one layer of the alien message it gives you x new keys to dive deeper in the message.
The data sets are any data sets - images, texts, schemes, math, models, whatever it might be.
Let say in the data set there is $n$ layers and $m_n$ possible keys in each layer. So potentially the message can be interpreted in $(m_n)^n$ meaningful ways.
On the picture, especially when it is small we see something which for us looks like something similar to eye picture, the human eye.
So for a human, it can be a meaningful information, but for someone else is just mosaic from smaller pictures(data sets) which in the particular case are different eye images but it can be any images(data sets).
So, not a human will not get a human key in the layer and the layer will be kinda transparent for another alien(not human), most likely for an alien the piece of information will be just a data set with no layers in it(they will not see that it is the picture of the pictures).
But a human will see the eye and it might be a key to interpreting the data set in a human way and as result get next human oriented layer of the information.
Alien sees nothing here, except - yeah there is some kind of information, we understand that but we have no clue how to interpret it, and for them, the particular piece of information will be the dead end in decrypting the whole set.
Which keys get those who decrypt the main data set will depend on who they are. And the whole dataset with all those layers will form an n-dimension maze, and the path trough the maze will be different for different species, humans, rocks whatever - those who decrypts the information.
And that allows the aliens to encrypt different information for different aliens, in one message.
Beauty is in the eye of the beholder
Which information opens depend on the interpretation, the particular combination of keys, and probably the sequence in which they were obtained - all that will determine the result, the "message".
But what if one sees let's say 2 keys.
On the picture, it is the matter of your own preference what to see. You can interpret it in any way (there is a lot of such pictures on the internet I just took first from the list). There 3 sets of stories about the picture, one set perfectly fit one interpretation, one set fit another interpretation, one set which fits both or neither.
Same is with ideas interpretations, the story Shakespeare in the Bush - true or not, but the difference in interpretations of an idea may lead to different actions.
Same story in any dataset. One can see the things he likes to see in the data set. And may prefer one interpretation over another interpretation, by working with the information which he likes more. The choose can be conscious or unconscious it is not important, but the choice itself defines the preference of the decoder.
By !preference we define not preferred stuff and do it the same way trough the moving on the path of preferences maze.
The aliens can create the message for different types of aliens, even without knowing them, possible with the use of the modeling system from another alien related answer Aliens are on their way. What can cause them to not understand us?
So yes, if aliens have emotions, we can transfer them the message which will have the proper translation of emotions, including our translation of politeness into their emotions and concepts.
So yes it is possible to send emotions, and do it even in the way they will not think that you smile but have a knife in another hand.
But mostly I agree with @Tharaib's answer, it is complicated and not very much needed.
Send them information about presence - polite invitation
Send them schemes of a magical power device, working in the way they will discover later, after they will have critical mass of those devices, that it will explode in 100 years all at once - it will be kinda demand - you have 50 years to fly to us, and try to get proper information how to stop collapse of your civilisation, your move.
It is possible that after decryption, there will be a hologramme of George Washington in his national costume on pure english(better than my) will polite invite the human civilisation to the aliens.