21.2. Results of the automated data classification

The data was classified using a degree of roughness of 0.3 (a quite detailed description of cases) and rule precision threshold of 0.5 (rather general rules). The rules generated by the rough sets system and the attribute strength report are given in Tables 14 and 15. Please note, that the ranges of parameter values given in Table 14 are only interpretable for this particular experiment and are presented here only for completeness of the result presentation.

The correctness of the data classification was tested additionally using the leave-one-out method. As mentioned above, the verification of the results is possible only for non-rough models. The error rate of the leave-one-out verification of the data classification for precise model is about 8%, which is a good result that demonstrates both the high predictive capability of the parameters used and the strong dependency patterns (Reduct System, 1993).

Table 14: Results of the rule generation using the rough sets method. System setup: Roughness=0.30, Rule Precision Threshold= 0.50. Abbreviations: f0std - standard deviation of F0 [Hz], ectm - relative duration of the end of closing [%],sctm - relative duration of the start of closing [%], otm - relative duration of open phase [%], eotm - relative duration of the end of opening [%], soam - start of opening slope, ecam - end of closing slope, peakm - peak-to-peak amplitude, opvm - variation of the open phase.
decision	rule
group==> control	[15.70< sotm<=24.10] & [13.24< otm<=21.52] & [604.80< ecam<=1717.40] | OR | |[15.70< sotm<=24.10] & [13.24< otm<=25.65] & [882.95< ecam<=1717.40]
group==> breathy	|[scam>120.01] & [21.52< otm<=38.06] & [ecam>1161.10] & [133.64< f0m<=223.94] | OR | |[scam>120.01] & [ecam>1161.10] & [133.64< f0m<=205.88] | OR | |[21.52< otm<=38.06] & [1252.50< opvm<=2058.50] & [205.88< f0m<=223.94] | OR | |[scam>120.01] & [otm<=21.52 or otm>38.06] & [ecam>1161.10] & [1252.50< opvm<=2058.50] & |[f0m<=205.88 or f0m>223.94] | OR | |[scam<=120.01] & [21.52< otm<=38.06] & [205.88< f0m<=223.94]
group==> rp-with-comp	| |[f0std<=9.87 or f0std>72.35] & [(3.87< ectm<=5.76) or (7.66< ectm<=9.55)]& |[sctm<=17.08 or sctm>43.80] | OR | |[f0std<=9.87 or f0std>72.35] & [3.87< ectm<=9.55] & [sctm<=17.08 or | | |sctm>43.80] & [4.97< otm<=25.65] | OR | |[eotm<=16.82] & [25.65< otm<=33.93] | OR | |[eotm<=16.82] & [3.87< ectm<=5.76] | OR | |[f0std<=9.87 or f0std>72.35] & [eotm>16.82] & [17.08< sctm<=30.44] & | | |[otm<=4.97 or otm>33.93] | OR | |[3.87< ectm<=9.55] & [30.44< sctm<=43.80] & [otm<=4.97 or otm>25.65]
group==> rp-without-c	|[soam>-185.44] & [79.46< f0m<=115.58] | |OR ||[ecam<=326.65] & [soam>-185.44] & [8115.00< peakm<=19710.00] & [f0m>115.58] | |OR | |[ecam<=326.65] & [18.79< f0std<=54.50] & [peakm<=8115.00 or peakm>19710.00] | OR | |[18.79< f0std<=54.50] & [ectm<=7.66 or ectm>17.12] | OR | |[ecam>326.65] & [7.66< ectm<=17.12] & [8115.00< peakm<=19710.00]
group==> chordectomy	|[ctm<=7.80 or ctm>12.03] & [9.87< f0std<=72.35] & [sotm<=11.51] | OR ||[ecam>326.65] & [ctm<=7.80 or ctm>12.03] & [9.87< f0std<=81.27] | OR | |[otm<=8.90] & [7.80< ctm<=12.03] | OR | |[otm<=8.90] & [f0std<=9.87 or f0std>81.27] | OR | |[otm<=8.90] & [sotm>15.70] | OR | |[ecam<=326.65] & [7.80< ctm<=12.03] & [9.87< f0std<=81.27] & [sotm>11.51] | OR | |[ecam<=326.65] & [ctm<=7.80 or ctm>12.03] & [f0std<=9.87 or f0std>72.35] & | | |[sotm>11.51]

Table 15: Attribute strength report of the rules in Table 14. System setup and abbreviations are as used in Table 14.
decision	coverage	attribute	relative parameter strength
group==> control	100 %	otm	0.71
		ecam	0.71
		sotm	0.56
group==> breathy	100 %	scam	0.5
		otm	0.48
		f0m	0.48
		ecam	0.46
		opvm	0.42
group==> rp-with-comp	100 %	ectm	0.54
		sctm	0.44
		otm	0.42
		f0std	0.35
		eotm	0.29
group==> rp-without-c	100 %	f0m	0.46
		ecam	0.44
		f0std	0.42
		soam	0.40
		ectm	0.35
		peakm	0.35
group==> chordectomy	100 %	f0std	0.65
		sotm	0.56
		ecam	0.54
		otm	0.54
		ctm	0.46

The parameter strength report (the relative importance of the parameter for the validation of a given rule) reveals interesting results (Table 15). For example, in the hierarchy of the factors needed for the proper classification of breathy voice, the most important one is the duration of the no-contact phase, followed by the steepness of the start of the contact rise phase (start of closing), F0 and the steepness of the second part of the contact rise (end of closing). Comparing the factors that are important for classifying the cases, one can see that the steepness of the closing phase occurs in all rules. Duration of the closing and opening phases, peak-to-peak amplitude, its variation and duration of the opening phase also play important roles in this deterministic classification of data.

That is a screen shot from Datalogic (Reduct System) program: