Can I still try to publish my work if my algorithm's results are not as good as other algorithms'?
If you want to get technical, in general no learning algorithm performs any better than any other.

The question then, is what can be learned from your algorithm.  In your question, you speak of it as a fond intellectual child that you wish to grow and nurture, and you speak of your personal concerns about acceptance and rejection.  Here is the thing, though: none of that matters for a publication.  What matters is this: what new knowledge or capability is brought into the world with your work on your algorithm, and how can this be objectively evaluated?

Here are some possibilities that I can see:


Your algorithm may perform better on an interesting and useful class of problems, and thus be of practical interest.
Your algorithm may perform worse, but have some other desirable property, such as executing very quickly or using very little memory, in which case the performance comparison just needs to show that it is sufficient, and you can show much better performance with regards to those other properties.
Your algorithm may perform worse, but do so in a way that is enlightening, e.g., taking a more human-like approach, or showing how something can be accomplished by a very unusual and unexpected route.  In this case, the performance comparison is simply showing that your algorithm does not perform too badly to be interesting, and the narrative should focus on the path taken to achieve your results and why that is interesting.
Your algorithm may only have taught you personally some interesting things about classification and scientific research, in which case you should mourn the passing of a fine research idea and move on with your life.


Only you and those who know your work well will be able to tell which category it truly fits into.