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Table 4 Macro-F1 scores for missing event prediction in empirical datasets. We highlight in bold the two best scores for each dataset. For baseline models we underline their highest score

From: Time-varying graph representation learning via higher-order skip-gram with negative sampling

Model

Operator

Dataset

LyonSchool

SFHH

LH10

Thiers13

InVS15

DyANE

Average

56.8 ± 0.6

50.6 ± 0.8

51.3 ± 1.0

49.1 ± 0.6

49.3 ± 0.8

Hadamard

87.3 ± 0.3

73.5 ± 0.6

\(\underline{67.0}\pm 1.0\)

\(\underline{87.2}\pm 0.3\)

\(\underline{80.1}\pm 0.8\)

Weighted-L1

87.8 ± 0.3

73.3 ± 0.6

65.9 ± 1.0

84.0 ± 0.4

78.4 ± 0.6

Weighted-L2

\(\underline{88.5}\pm 0.2\)

\(\underline{73.7}\pm 0.5\)

66.1 ± 1.0

84.4 ± 0.4

78.9 ± 0.6

Concat

64.4 ± 0.5

52.4 ± 0.8

51.9 ± 1.0

57.0 ± 0.6

51.4 ± 0.7

DynGEM

Average

56.2 ± 0.5

\(\underline{51.8}\pm 0.8\)

\(\underline{52.0}\pm 1.1\)

49.7 ± 0.5

50.9 ± 0.7

Hadamard

54.8 ± 0.6

51.3 ± 0.7

51.7 ± 1.2

44.7 ± 0.7

\(\underline{50.9}\pm 0.6\)

Weighted-L1

55.5 ± 0.4

48.5 ± 0.8

50.2 ± 1.0

\(\underline{52.2}\pm 0.4\)

49.8 ± 0.7

Weighted-L2

53.2 ± 0.7

47.8 ± 0.9

48.0 ± 1.1

48.9 ± 0.6

45.3 ± 0.6

Concat

\(\underline{58.2}\pm 0.5\)

50.4 ± 0.8

46.4 ± 1.4

48.8 ± 0.5

49.9 ± 0.6

DynamicTriad

Average

51.4 ± 0.4

52.6 ± 0.6

53.0 ± 0.8

52.0 ± 0.4

49.9 ± 0.7

Hadamard

53.1 ± 0.4

49.5 ± 0.6

52.0 ± 0.8

51.7 ± 0.5

49.8 ± 0.6

Weighted-L1

64.3 ± 0.4

56.6 ± 0.7

54.2 ± 0.9

53.6 ± 0.4

47.2 ± 0.6

Weighted-L2

\(\underline{64.5}\pm 0.4\)

\(\underline{57.3}\pm 0.7\)

\(\underline{54.9}\pm 0.9\)

\(\underline{54.5}\pm 0.5\)

47.0 ± 0.6

Concat

52.6 ± 0.3

51.8 ± 0.5

52.7 ± 0.9

51.5 ± 0.3

\(\underline{49.9}\pm 0.6\)

DySAT

Average

51.3 ± 0.4

51.6 ± 0.6

52.5 ± 0.8

50.0 ± 0.4

50.3 ± 0.6

Hadamard

\(\underline{73.8}\pm 0.6\)

\(\underline{52.5}\pm 0.7\)

56.6 ± 0.7

\(\underline{68.5}\pm 0.5\)

61.5 ± 0.8

Weighted-L1

71.3 ± 0.5

52.0 ± 0.6

\(\underline{57.6}\pm 0.8\)

63.2 ± 0.6

\(\underline{64.4}\pm 0.5\)

Weighted-L2

70.7 ± 0.5

51.5 ± 0.7

56.5 ± 0.8

63.1 ± 0.5

63.4 ± 0.5

Concat

49.2 ± 0.4

48.8 ± 0.8

52.4 ± 0.9

49.8 ± 0.5

50.4 ± 0.6

ISGNS

Average

52.4 ± 0.6

49.5 ± 0.8

44.9 ± 0.9

48.0 ± 0.4

42.7 ± 0.8

Hadamard

79.8 ± 0.4

59.3 ± 0.7

61.1 ± 1.2

59.3 ± 0.6

\(\underline{51.7}\pm 0.7\)

Weighted-L1

80.8 ± 0.3

59.8 ± 0.7

61.7 ± 1.0

59.0 ± 0.6

49.8 ± 0.7

Weighted-L2

\(\underline{81.5}\pm 0.3\)

\(\underline{60.2}\pm 0.7\)

\(\underline{62.5}\pm 0.9\)

\(\underline{59.9}\pm 0.6\)

51.5 ± 0.7

Concat

55.8 ± 0.7

50.8 ± 0.6

46.8 ± 0.8

52.2 ± 0.5

48.5 ± 0.6

\(\text{HOSGNS} ^{(\text{stat})}\)

Hadamard

52.1 ± 0.4

43.8 ± 0.6

34.2 ± 0.2

55.9 ± 0.6

43.0 ± 0.5

\(\text{HOSGNS} ^{(\text{dyn})}\)

Hadamard

89.2 ± 0.2

74.9 ± 0.6

67.1 ± 0.8

90.7 ± 0.3

81.4 ± 0.5

\(\text{HOSGNS} ^{(\text{stat}|\text{dyn})}\)

Hadamard

89.2 ± 0.3

76.3 ± 0.7

68.5 ± 1.0

89.9 ± 0.3

80.8 ± 0.6