# understanding of effect of $\alpha$ in Dirichlet distribution

When reading the topic modeling tutorial written by Blei, KDD 2011 tutorial I was confused about a set of diagrams which aim to show the effect of $\alpha$ in Dirichlet distribution.

For example, for the plot with $\alpha=1$, what am I suppose to discover? What does item mean here? Do those 15 items mean a 15-dimensional probability vector? The $\alpha=1$ is assumed to lead to a uniform distribution. But I feel confused about how to connect this plot with a uniform distribution. I also list other plots with $\alpha=100$ and $\alpha=0.01$.

$\alpha$ is the prior controlling how much you weigh previously selected groups when selecting a new group assignment.
As $\alpha$ gets smaller you weigh previously selected groups more heavily, hence for $\alpha=0.1$ only a few groups are selected. As $\alpha$ gets larger you weigh the previously selected groups less and less, hence the uniform distribution of groups for $\alpha=100$.
Note $\alpha=1$ corresponds to a uniform prior for the number of groups, but the resulting distribution will not be uniform. In general, larger $\alpha$ equals more groups, smaller $\alpha$ equals less groups.
• Thanks! Could I understand the graph this way. These plots related to a scenario with 15 items and 10 groups. Using $\alpha=0.1$ as an example, here item 1 is more likely to be assigned to group 7 with pmf almost equal to 1; while item 2 more likely to be assigned to group 9 and group 6, where group 9 with pmf almost equal to 0.8 and group 6 with pmf almost equal to 0.2. – user3269 Apr 30 '14 at 3:26