Question abou sub graph

[KwankiAhn]

Hello, I'm a newbie with GNN and interested in Recommender system using Graphs. Thanksfully I found a nice paper IGMC.

I 'm trying to understand 'generating sub graph' of this code, What I was doing was:

1. generate csr with example picture of rating

row = np.array([0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6])
col = np.array([0, 1, 2, 4, 8, 4, 6, 7, 1, 3, 4, 6, 0, 6, 7, 8, 2, 3, 5, 7, 9, 1, 3, 5, 8, 0, 2, 5, 7, 9])
rat = np.array([1, 2, 5, 2, 4, 4, 5, 2, 1, 4, 3, 5, 5, 5, 1, 2, 1, 2, 5, 5, 4, 1, 4, 4, 1, 5, 4, 3, 2, 5])
rat = rat - 1  # value to index
ACsr = ssp.csr_matrix((rat, (row, col)))
※ these values are just same with picture of your example rating table.

('
 	with 30 stored elements in Compressed Sparse Row format>,
 array([[0, 1, 4, 0, 1, 0, 0, 0, 3, 0],
        [0, 0, 0, 0, 3, 0, 4, 1, 0, 0],
        [0, 0, 0, 3, 2, 0, 4, 0, 0, 0],
        [4, 0, 0, 0, 0, 0, 4, 0, 1, 0],
        [0, 0, 0, 1, 0, 4, 0, 4, 0, 3],
        [0, 0, 0, 3, 0, 3, 0, 0, 0, 0],
        [4, 0, 3, 0, 0, 2, 0, 1, 0, 4]]))

2. Then I get a batch sample

• dataset_class = 'MyDynamicDataset'

Batch(x=[120, 4], edge_index=[2, 112], y=[30], edge_type=[112], batch=[120], ptr=[31])

edge_index (2, 116)
y (30,)
edge_type (116,)

edge_index [[  1   0   2   3   4   7   9   8  10  11  13  12  14  15  17  16  18  19
   21  20  22  23  25  24  26  27  29  28  30  31  33  32  34  35  37  36
   38  39  41  40  42  43  45  44  46  47  49  49  50  51  53  53  54  55
   57  56  58  59  65  64  66  67  69  68  70  71  73  72  74  75  77  76
   78  79  81  80  81  82  83  83  85  85  86  87  89  88  89  90  91  91
   93  94  97  96  98  99 101 100 102 103 104 105 107 107 109 108 110 111
  112 115 117 116 117 118 119 119]
 [  2   3   1   0   7   4  10  11   9   8  14  15  13  12  18  19  17  16
   22  23  21  20  26  27  25  24  30  31  29  28  34  35  33  32  38  39
   37  36  42  43  41  40  46  47  45  44  50  51  49  49  54  55  53  53
   58  59  57  56  66  67  65  64  70  71  69  68  74  75  73  72  78  79
   77  76  82  83  83  81  80  81  86  87  85  85  90  91  91  89  88  89
   94  93  98  99  97  96 102 103 101 100 107 107 104 105 110 111 109 108
  115 112 118 119 119 117 116 117]]
y [1. 2. 5. 2. 4. 4. 5. 2. 1. 4. 3. 5. 5. 5. 1. 2. 1. 2. 5. 5. 4. 1. 4. 4.
 1. 5. 4. 3. 2. 5.]
edge_type [3 3 3 3 3 3 2 0 2 0 2 0 2 0 0 0 0 0 1 0 1 0 3 2 3 2 0 3 0 3 0 2 0 2 0 1 0
 1 0 2 0 2 3 2 3 2 3 0 3 0 3 0 3 0 3 3 3 3 3 3 3 3 2 2 2 2 1 0 1 0 0 0 0 0
 3 3 0 3 3 0 0 2 0 2 0 2 3 0 2 3 1 1 2 2 2 2 3 3 3 3 3 2 3 2 3 3 3 3 1 1 2
 0 3 2 0 3]
ADJ (120, 120) [[0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0]
 [0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0]
 [4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0]

Can you provide how ADJ is acquired ?

• rating was 30 originally, but we got edge_index : (2, 116), edge_type (116,)
• what these are meaning ?

[muhanzhang]

Hi! A batch contains multiple disconnected subgraphs, which are compressed into one single block-diagonal adjacency matrix ADJ by PyTorch Geometric. Your original ACsr is the observed graph from which you extract subgraphs around ratings. Depending on what links you feed, you will get different subgraphs extracted from ACsr by the subgraph_extraction_labeling() function. Then you will get different batches.