I do think that those 90 columns of binary data can be reduced to some smaller number of columns, so that the computational time can be reduced significantly
This assumption seems unfounded to me. Since the computational time of calculating pairwise dissimilarities corresponds O(n^2) the effect of dimensionality reduction will be merely noticeable. I mean if it takes two days, you wouldn't mind 2-3 hours less.
What I have in mind is
Do you really need all pairwise dissimilarities? Often one actually doesn't. Therefore a spatial index can be used.
If you do need them all: Do you need to update them often? How about keeping the dissimilarities. Adding a single item will take few time
Anyway you should try to reformulate the problem. 10 or 100 variables will make little difference in accomplishing your current approach.
It's not about not being able to compute something.
Distances much be used to measure something meaningful. This will fail much earlier with categorial data. If it ever works with more than one variable, that is...
If you have the attributes shoe size and body mass, Euclidean distance doesn't make much sense either. It's good when x,y,z are distances. Then Euclidean distance is the line of sight distance between the points.
Now if you dummy-encode variables, what meaning does this yield?
Plus, Euclidean distance doesn't make sense when your data is discrete.
If there only exist integer x and y values, Euclidean distance will still yield non-integer distances. They don't map back to the data. Similarly, for dummy-encoded variables, the distance will not map back to a quantity of dummy variables...
When you then plan to use e.g. k-means clustering, it isn't just about distances, but about computing the mean. But there is no reasonable mean on dummy-encoded variables, is there?
Finally, there is the curse of dimensionality. Euclidean distance is known to degrade when you increase the number of variables. Adding dummy-encoded variables means you lose distance contrast quite fast. Everything is as similar as everything else, because a single dummy variable can make all the difference.
Best Answer
According to my knowledge, you should either normalize or standardize the whole feature vector. If you keep the numeric values standardized and the categorical variables as they are , then they could cause a large variance in the vector. Another option is to standardize the numeric values and normalize the categorical values.
AND
If they are in a range other than 0-1 then it is better to normalize them in the range 0-1.