A Bayesian Allocation Model Based Approach to Mixed Membership Stochastic Blockmodels

Figures & data

Figure 1. Comparison of MMSB graphical models: (a) Traditional (b) Graphical model in BAM notation.

Figure 2. Count tensor representation of a binary adjacency matrix.

Table 1. $K_{est}$ estimations in 50 experiments for three different connectivity levels. From top to down, the connectivity parameter $\in$ takes values of $\{0.9,0.7,0.5\}$ respectively.

BAM-MMSB						MMSB
K	1	2	3	4	5	1	2	3	4	5
2	0	50	0	0	0	0	50	0	0	0
3	0	0	50	0	0	0	2	43	5	0
4	0	0	0	50	0	0	2	22	25	0
2	0	50	0	0	0	0	49	1	0	0
3	0	0	50	0	0	0	7	39	4	0
4	0	0	0	50	0	0	3	28	19	0
2	0	50	0	0	0	0	50	0	0	0
3	0	0	50	0	0	0	33	16	1	0
4	0	0	0	50	0	0	38	12	0	0

Table 2. Ratio of correct estimations with respect to total estimations out of 50 replicates for $\in =0.5$.

LEM	HMM	MFM-SBM	MMSB	BAM-MMSB
0.98	1	0.98	1	1

Figure 3. Estimated number of blocks $K_{opt}$ as the scaling factor $N_{ij}$ for each index is increased.

Figure 4. Weighted pseudocounts of the contingency tensor for each weighting scheme.

Figure 5. The selected number of blocks for benchmark networks. The top and bottom row illustrate the results for (i) uniform and (ii) source-dest.

Table 3. Estimated number of clusters for dolphin data.

Method	LEM	HMM	MFM-SBM	MMSB	BAM-MMSB
Number of clusters	5	5	2	2	2