關聯規則挖掘之apriori演算法

前言：

眾所周知，關聯規則挖掘是資料探勘中重要的一部分，如著名的啤酒和尿布的問題。今天要學習的是經典的關聯規則挖掘演算法——Apriori演算法

一、演算法的基本原理

由k項頻繁集去匯出k+1項頻繁集。

二、演算法流程

1.掃描事務資料庫，找出1項集，並根據最小支援度計數，剪枝得出頻繁1項集。k=1.

2.由頻繁k項集進行連線步操作，形成候選的k+1項集，並掃描資料庫，得出每一項的支援度計數，並根據最小支援度計數，剪枝得到頻繁k+1項集。

迭代的進行第2步直到頻繁k項集是空的。

3.由頻繁項集構造關聯規則。先列出所有可能的關聯規則，然後計算相應的置信度，最終篩選出滿足最小置信度的強關聯規則。

三、演算法實現

測試資料集：data.txt

1, 7, 15, 44, 49
2, 1, 19
3, 1, 19
4, 3, 4, 15, 18, 35, 44
5, 2, 4, 7, 9, 23
6, 14, 21, 44
7, 4, 12, 31, 36, 44, 48
8, 15, 27, 28
9, 2, 28
10, 3, 18, 35
11, 23, 24, 40, 41, 43
12, 20, 43, 48
13, 49
14, 1, 19, 26
15, 5, 22, 39
16, 16, 32, 45
17, 4, 6, 9, 10, 16, 22
18, 1, 19, 23
19, 7, 11, 37, 45
20, 3, 18, 32, 35
21, 1, 8, 19, 47
22, 34, 39, 44
23, 13, 19
24, 4, 9, 38
25, 7, 22, 48
26, 7, 11, 14
27, 23, 24, 40, 41, 43
28, 9, 14
29, 0, 2, 42
30, 13, 35
31, 23
32, 8, 21, 25, 38
33, 4, 46
34, 23, 24, 40, 41, 43
35, 4, 17, 29, 47
36, 12, 31, 36
37, 14, 22, 26, 37, 44
38, 0, 16, 30, 32, 45, 47
39, 1, 11, 19, 25, 27, 29, 46
40, 15, 16, 18, 21, 26
41, 4, 10, 14
42, 3, 36
43, 23, 27, 28
44, 15, 21, 40
45, 10, 19, 25, 32
46, 11, 22, 44
47, 8
48, 0, 2, 46
49, 33, 42
50, 28, 39
51, 7, 17, 28
52, 1, 19
53, 32, 34
54, 0, 2, 46
55, 15, 30, 45
56, 39, 49
57, 46
58, 4, 9, 19
59, 0, 2, 16, 19, 46
60, 17, 21, 40
61, 2, 4, 6, 9, 39
62, 23, 24, 40, 41, 43
63, 13, 27, 28
64, 40
65, 12, 14, 44
66, 27, 28
67, 1, 36
68, 12, 31, 36, 48
69, 3, 18, 35
70, 5, 12, 16
71, 30, 49
72, 7, 29, 30
73, 17, 19, 30
74, 1, 13, 36
75, 19, 33, 49
76, 1, 5, 14, 38
77, 31
78, 1, 5, 8, 14, 22, 26
79, 7, 27, 30, 36, 37, 43
80, 13, 35, 42
81, 5, 22, 32
82, 7, 11, 20, 28, 37, 45
83, 23, 24, 40, 41
84, 3, 5, 14, 22, 36
85, 12, 31, 36, 48
86, 45
87, 12, 31, 36, 48
88, 14, 44
89, 5, 19, 22, 34, 43
90, 0, 2, 45, 46
91, 16, 32, 45, 47, 48
92, 1, 48
93, 1, 3, 18, 35
94, 7, 11, 37, 45
95, 16, 26, 32, 41, 45
96, 1, 29, 30
97, 1, 19
98, 1
99, 14, 22, 37
100, 22, 34, 40
101, 31
102, 16, 17, 43
103, 8, 19, 20, 48
104, 1, 12, 15, 27, 31, 34, 36, 48
105, 3, 40, 45
106, 13, 18, 21, 41, 47, 48
107, 3, 18, 22, 27
108, 6, 16, 17, 31, 33, 42
109, 5, 22, 27, 35
110, 7, 15, 49
111, 6, 12, 26, 29, 31, 32, 36, 48
112, 11, 13, 14, 44
113, 23, 33, 35
114, 5, 8, 18, 29, 46
115, 41
116, 1, 3, 8, 27, 28
117, 1, 11, 19, 33
118, 23, 24, 40, 41
119, 16, 18, 23, 27, 29, 30, 40, 49
120, 14, 18, 44
121, 0, 2, 46
122, 3, 18, 35
123, 12, 31, 36, 48
124, 7, 11, 20, 29, 37, 45
125, 2, 24, 27
126, 5, 13, 22
127, 22, 42, 46, 47
128, 39, 41
129, 13, 23
130, 1, 24, 40, 42
131, 14, 20, 26, 44
132, 12, 31, 36, 48
133, 7, 21, 27, 28, 33, 36, 47
134, 17, 29, 47
135, 12, 31, 36
136, 4, 9, 11
137, 3, 11, 14, 18, 29, 35
138, 20, 33, 42
139, 22, 44, 46
140, 5, 6, 16, 22, 33, 38, 49
141, 0, 2, 12, 24, 26, 31, 46
142, 0, 6, 25
143, 5, 19, 22
144, 11, 13, 14, 35, 48
145, 17, 29, 35, 44, 47
146, 7, 15
147, 5, 22
148, 0, 1, 2, 46
149, 4, 9, 18, 41
150, 1, 12, 18, 19, 39
151, 0, 2, 19, 22, 46
152, 33, 37, 42
153, 0, 2, 37, 46
154, 11, 18, 35, 45
155, 4, 9, 15
156, 19, 24, 28, 35, 49
157, 5, 22, 37
158, 0, 2, 5, 19, 33, 35, 39, 46
159, 3, 4, 5, 48
160, 4, 6, 18, 28, 35
161, 3, 18, 31, 35
162, 6, 17, 25, 49
163, 17
164, 3, 8, 9, 20, 22, 23, 42
165, 4, 15, 17, 21, 26, 36, 48
166, 14, 41, 44
167, 19, 28, 42
168, 4, 9
169, 13, 31, 33, 41, 42
170, 5, 22, 28
171, 0, 16, 32
172, 5, 28, 43
173, 24, 36, 37, 42
174, 31
175, 40, 42
176, 11, 34, 48
177, 14, 28, 40, 43
178, 0, 13, 26
179, 16, 32, 45
180, 10, 14, 44, 46
181, 4, 7, 9, 19, 36
182, 23, 24, 40, 41, 43
183, 4, 9, 37
184, 5, 22, 31
185, 21, 24, 29
186, 0, 6, 22, 46
187, 3, 18, 21, 35, 39, 46
188, 12, 31, 36, 38, 48
189, 28
190, 23, 24, 40, 41, 43
191, 12, 24
192, 6, 27, 28
193, 23, 24, 40, 41, 43
194, 27, 28
195, 5, 14, 16, 22
196, 5, 22
197, 27, 28, 44, 47
198, 5, 22
199, 0, 2, 46
200, 0, 10, 30
201, 15, 33, 42
202, 4, 9, 40
203, 1, 36
204, 23, 24, 40, 41
205, 25, 27, 28, 32
206, 7, 11, 37, 45
207, 20, 48
208, 7, 11, 37, 45
209, 9, 27, 28
210, 7, 11, 37
211, 1, 2, 9, 22, 48
212, 7, 27, 39, 45
213, 1, 6, 8, 15, 18, 19, 21, 42
214, 23, 24, 40, 41
215, 4, 14, 20, 32, 36, 44
216, 16, 32, 45
217, 18, 26, 42, 45
218, 2, 11, 23
219, 11, 15, 35
220, 31, 39, 43, 45, 46
221, 0, 2, 28, 40, 46
222, 13, 24, 26, 35, 39, 47
223, 7, 21, 23, 30, 36
224, 23, 40, 47
225, 5, 22
226, 1, 5, 19, 30
227, 7, 15, 49
228, 7, 11, 37, 45
229, 23, 31, 34, 45
230, 7, 29, 48
231, 27, 28
232, 24, 44
233, 4, 5, 9, 39
234, 5, 22, 25, 28, 34, 46
235, 23, 32, 48
236, 16, 42
237, 5, 22
238, 4, 9, 15, 25
239, 1, 12, 16, 17, 19, 26, 48
240, 1, 3, 16, 19, 35
241, 11, 12
242, 4, 9, 10, 12, 45
243, 12, 31, 36, 46, 48
244, 17, 28, 47
245, 3, 18, 35
246, 4, 9
247, 7, 11, 37, 45
248, 5, 12, 22
249, 6, 14, 38, 48
250, 9, 10, 34, 36, 42
251, 3, 18, 35
252, 3
253, 14, 27
254, 0, 1, 19
255, 3, 18, 24, 35
256, 12, 31, 36, 48
257, 19, 31, 41
258, 1, 11, 14, 32, 34, 35
259, 5, 14, 28, 39, 49
260, 9, 14, 21, 46
261, 6
262, 5, 22, 31
263, 11, 40
264, 0, 2, 46
265, 23, 24, 40, 41, 43
266, 3, 14, 23, 44
267, 18, 22, 42, 49
268, 3, 24
269, 12, 31, 36, 48
270, 20, 25, 27
271, 15, 30, 39
272, 7, 15, 49
273, 12, 31, 36, 48
274, 16, 18, 32, 42
275, 27, 31, 33, 42
276, 5, 9, 22, 43
277, 2, 4, 36, 40, 41, 48
278, 19, 28, 30, 32
279, 2, 31, 39, 44
280, 1, 2, 19, 21, 23, 28, 45
281, 7, 10, 14, 16, 23, 32, 45
282, 4, 9, 14, 36, 44
283, 21, 29
284, 9, 13, 17, 46
285, 38, 39
286, 1, 8, 19
287, 0, 33, 42
288, 2, 33, 36, 47
289, 12, 31, 36
290, 28
291, 16, 27, 28
292, 7, 15, 49
293, 8, 21, 24, 33, 34, 40, 42, 44
294, 1, 14, 26, 32, 41
295, 23, 33, 42
296, 14, 21, 23, 24
297, 0, 2, 46
298, 11, 29
299, 1, 23, 33, 42, 47
300, 16, 32, 45
301, 3, 4, 9, 33, 37, 43
302, 19, 25, 30, 43, 46
303, 0, 2, 46
304, 16, 17, 34
305, 5, 21, 22, 25, 27, 31, 42
306, 5, 12, 16, 31, 36
307, 8, 22, 42
308, 3, 27, 36
309, 16, 32, 45
310, 12, 31, 36, 48
311, 5, 22
312, 7, 11, 37, 45
313, 9, 13, 20, 21, 24, 39, 41, 45
314, 1, 9, 15, 24, 37
315, 4, 9
316, 18, 35, 45
317, 0, 2, 46
318, 5, 10, 14, 47
319, 1, 4, 10, 14, 25, 36, 49
320, 12, 34
321, 7, 15, 49
322, 23, 28
323, 1, 19
324, 0, 2, 46
325, 1, 2, 19
326, 7, 11, 37, 45
327, 29, 33, 38, 45, 48
328, 4, 9, 24
329, 1, 19, 23, 30, 44
330, 5, 13
331, 12, 31, 36, 48
332, 0, 2, 46
333, 5, 14, 20, 24, 28, 31, 39, 46
334, 4, 9, 13, 33, 43, 46
335, 5, 14, 22, 29
336, 2, 8, 10, 19, 35, 45
337, 14, 24, 34, 44
338, 5, 22, 28, 30, 47
339, 0, 28, 47
340, 7, 15, 49
341, 5, 9, 28, 41
342, 1, 7, 11, 37
343, 26
344, 44
345, 0, 2, 46
346, 5, 10, 26, 30
347, 8, 12, 14, 33, 44, 47
348, 3, 4, 27, 42
349, 9, 11, 40, 45
350, 3, 4, 9, 11, 12, 47
351, 5, 22, 35
352, 26, 29, 45
353, 4, 9, 31
354, 0, 13, 27, 28, 31, 36
355, 17, 32, 47
356, 1, 31, 41
357, 14, 43, 44
358, 18, 35
359, 5, 10, 16
360, 33, 37
361, 4, 30, 31
362, 9, 14, 25
363, 14, 44
364, 23, 27, 28
365, 9, 18, 22
366, 5, 8, 22
367, 10, 29
368, 3, 15, 16, 20, 33, 45
369, 4, 8, 12, 25, 34
370, 9, 26, 28
371, 7, 9, 15, 49
372, 3, 48, 49
373, 5, 21, 30, 31, 43
374, 4, 9
375, 1, 19, 28
376, 4, 9, 26, 33, 47
377, 1, 13, 19, 41
378, 15, 18, 41
379, 14, 28, 48
380, 5, 22, 47
381, 49
382, 7, 15, 49
383, 8, 28, 47
384, 8, 25, 29
385, 0, 4, 10, 21
386, 41
387, 5, 23, 26, 44
388, 25
389, 4, 9
390, 12, 17, 26, 29, 31, 47
391, 3, 18, 35
392, 7, 11, 34, 37, 45
393, 9, 13, 18, 23, 25, 33, 40
394, 15
395, 5, 17, 22, 40, 48
396, 23, 33, 46
397, 7, 15, 49
398, 16, 32, 45
399, 7, 15, 49
400, 1, 48
401, 2
402, 36, 39, 49
403, 3, 4, 10
404, 34, 36
405, 7, 17, 34, 35, 46
406, 5, 22
407, 32, 34, 36, 42
408, 14, 46
409, 3, 18, 29, 35, 37, 48
410, 27, 33, 42
411, 27, 28
412, 27, 28
413, 4, 9, 13, 21
414, 1, 5, 7, 10, 21, 22, 30, 31
415, 7, 15, 49
416, 4, 5, 14, 23, 42
417, 17, 29, 47
418, 30
419, 5, 33, 42
420, 27, 28, 31
421, 7, 15, 49
422, 16, 32, 45
423, 1, 2, 8, 25, 32
424, 12, 13
425, 16, 44
426, 0, 17, 24
427, 26
428, 4, 10, 27, 28, 43
429, 14
430, 4, 19, 47
431, 33, 42
432, 47
433, 8, 17, 23, 29, 43, 47
434, 0, 5, 33, 46
435, 9, 18, 35, 38, 40, 47
436, 2, 4, 11, 39
437, 4, 5, 9, 23, 24
438, 4, 24, 32
439, 8, 47
440, 2, 19
441, 2, 4, 9, 40
442, 0, 2, 46
443, 11, 19, 33, 42
444, 16, 32, 45
445, 5, 7, 22, 32, 42
446, 4, 33, 47
447, 19, 27, 36
448, 1, 28, 40
449, 23
450, 4, 9, 31, 33
451, 4, 28, 47
452, 25, 27, 34, 49
453, 3, 18, 35
454, 9, 27, 28
455, 14, 15, 35, 36
456, 14, 27, 28
457, 12, 16, 34
458, 0, 2, 13, 18, 24, 36, 46, 47
459, 14, 32, 44
460, 16, 32, 45
461, 2, 8, 16
462, 7, 15, 49
463, 14, 26, 30, 39, 44
464, 1, 23, 32
465, 0, 12, 20, 22, 49
466, 16, 20, 32, 49
467, 23, 24, 40, 41
468, 1, 3, 29, 41, 42, 43, 46
469, 5, 16, 25, 48
470, 17, 29, 47
471, 11, 16, 32, 45
472, 4, 9, 13
473, 17, 47
474, 11, 32
475, 12, 33, 42, 46
476, 23, 24, 40, 41
477, 9, 13, 14, 33, 38, 49
478, 14, 15, 26, 47
479, 3, 18, 35
480, 3, 21, 44
481, 3, 46
482, 9
483, 16, 24, 30, 31, 48
484, 19
485, 33, 42
486, 4, 34
487, 23, 24, 40, 41, 43
488, 5, 22
489, 10, 31
490, 4, 17, 40, 47
491, 39, 47
492, 14, 15, 31
493, 5, 26, 33, 42, 44
494, 13, 30, 38
495, 2, 3, 18, 35, 47
496, 12, 31, 36, 48
497, 17, 27, 28
498, 17, 29, 47
499, 14, 44
500, 0, 2, 46
501, 0, 21, 33, 39
502, 14, 27, 44
503, 12, 31, 36
504, 5, 18
505, 7, 11, 37, 45
506, 0, 20
507, 23, 30
508, 0, 14, 16, 32
509, 8
510, 13, 26, 27, 28, 46
511, 4, 9, 12, 17, 37
512, 10, 20, 37
513, 3, 7, 11, 21, 23
514, 21, 31, 32
515, 0, 1, 5, 23, 32, 42, 44
516, 0, 2, 46
517, 34, 37, 47
518, 16, 28, 32, 45
519, 3, 18, 35
520, 0, 5, 23, 33, 35, 46, 48
521, 14, 28, 29, 44
522, 13, 15, 24
523, 8, 22, 23
524, 11, 14, 26, 28, 41, 43, 45
525, 22, 39
526, 7, 11, 37, 45
527, 0, 2, 15, 16, 22, 35, 46
528, 41, 42
529, 6, 9, 30
530, 4, 13, 37, 45, 49
531, 0, 16
532, 14, 27, 28, 37, 48
533, 13, 28
534, 13, 18
535, 14, 29, 31, 35, 41, 49
536, 15, 34, 46, 48
537, 15, 28
538, 3, 18, 35
539, 12, 31, 36, 48
540, 33, 35, 42
541, 16, 32, 45
542, 7, 9, 15, 43
543, 7, 11, 37, 45
544, 12, 31, 36, 48
545, 14
546, 5, 8, 14, 21, 33, 38
547, 0, 3, 10, 38, 40
548, 10, 14, 18, 47
549, 11, 37, 38
550, 1, 3, 18, 19, 35
551, 3, 5, 22
552, 9, 24, 27, 34
553, 4, 7, 9
554, 0, 12, 35
555, 28, 29, 37
556, 9, 11, 28, 33, 41
557, 14, 44
558, 4, 11, 41, 43
559, 17, 47
560, 16, 20, 27, 32, 45
561, 2, 14, 42
562, 4, 9, 21, 43
563, 17, 29, 47
564, 23, 28, 33, 42
565, 6, 46
566, 3, 18, 35
567, 5, 9, 14, 18, 40
568, 4, 9, 34
569, 13, 14, 43, 44
570, 27, 28
571, 16, 32
572, 6, 14, 22
573, 0, 10, 41
574, 0, 18, 27, 31, 34, 37, 39, 47
575, 5, 7, 22
576, 4, 7
577, 7, 15, 49
578, 4, 15
579, 1, 16, 18, 20, 25, 29, 36, 46
580, 13, 30, 42
581, 24, 25, 31
582, 4, 7, 15, 18
583, 5, 22
584, 28
585, 23, 33, 42
586, 44
587, 15, 19, 27, 28
588, 0, 11, 18, 23, 47
589, 5, 22
590, 7, 11, 37
591, 7, 11, 37, 45
592, 6, 16, 33, 39, 42
593, 23, 24, 40, 41
594, 0, 9, 30, 31
595, 1, 32, 48
596, 2, 27, 28, 43
597, 1, 19
598, 35
599, 3, 10, 18, 35
600, 4, 9, 12, 48
601, 1, 6, 19
602, 7, 15, 49
603, 20, 22, 27
604, 13
605, 15, 16, 26
606, 3, 18, 35
607, 19
608, 5, 22
609, 1, 19
610, 12, 36, 37, 39
611, 2, 3, 10, 34
612, 30, 44
613, 13, 20, 22, 47
614, 4, 12, 26, 45
615, 13, 27, 35, 36
616, 0, 2, 46
617, 7, 10
618, 1, 2, 34, 39
619, 7, 11, 37, 45
620, 39, 43, 44
621, 3, 14, 30
622, 2, 12, 30, 32, 49
623, 1, 19, 32
624, 10, 21, 28, 31
625, 9, 17, 27, 28, 45
626, 10, 11, 16, 32
627, 12, 31, 36, 48
628, 3, 18, 29, 35, 40
629, 23, 24, 40, 41, 43
630, 14, 17, 29, 44, 47
631, 38
632, 0, 2, 46
633, 3, 18, 20, 35
634, 17, 29, 43, 47
635, 0, 6, 19, 26, 43
636, 3, 18, 35
637, 5, 21, 26, 27, 28, 39, 42, 49
638, 12, 31, 36, 48
639, 0, 2, 30, 46, 47
640, 5, 22, 33
641, 14, 33, 42
642, 0, 30, 43, 46
643, 11, 17, 35, 47
644, 0, 2, 46
645, 16, 32, 45
646, 20, 37, 39, 42
647, 14, 30, 44
648, 36, 39
649, 1, 17, 25, 37, 41, 49
650, 30, 36, 44
651, 12, 31, 36, 48
652, 24, 27, 28, 34, 39, 45, 48
653, 0, 37, 46
654, 18, 25, 44
655, 4, 9
656, 5, 22
657, 33, 42
658, 0, 26, 27, 28
659, 5
660, 2, 22, 33, 42
661, 7, 15, 49
662, 4, 9, 13, 17, 37
663, 5, 22, 35, 38, 47
664, 0, 2, 46
665, 27, 28, 39, 42
666, 12, 31, 36, 48
667, 27, 28
668, 16, 32, 45, 49
669, 21, 40
670, 5, 22, 48
671, 23, 33, 39, 42, 45
672, 1, 7, 25
673, 33, 42
674, 16, 19, 32, 38, 45
675, 7, 23, 30, 46
676, 42
677, 2, 10, 23, 42
678, 26, 30, 48
679, 7, 15, 49
680, 12, 25, 39, 48
681, 16, 17, 33, 47, 49
682, 49
683, 27, 45
684, 1, 11, 21, 42, 43
685, 8, 9, 22
686, 27, 28
687, 0, 2, 26, 43, 46
688, 16, 32, 45
689, 10, 22, 39
690, 7, 11, 14, 18, 23
691, 5, 22, 43
692, 17, 23, 29, 47
693, 1, 2, 15, 19
694, 7, 11, 37, 45
695, 5, 12, 22, 44
696, 8, 11, 22, 37
697, 20, 29
698, 7, 9, 11, 13, 37, 39, 45
699, 7, 11, 37, 45
700, 3, 36, 42, 49
701, 16, 32, 45
702, 21, 35
703, 0, 2, 46
704, 10, 18, 44
705, 6, 15, 21, 27, 28, 34, 41, 46
706, 7, 11, 37, 45
707, 16, 40
708, 37, 43
709, 7, 15, 29, 49
710, 12, 31, 36, 48
711, 5, 22, 24
712, 12, 13, 14, 32
713, 4, 5, 9, 32
714, 10, 40, 44
715, 3, 18, 35
716, 1, 13, 20, 31, 45
717, 37, 47, 48
718, 4, 9
719, 1, 19
720, 4, 12, 31
721, 10, 33
722, 14, 44
723, 5, 15, 34
724, 23, 36
725, 5, 29, 32, 35, 42
726, 3, 11, 29
727, 4, 6, 8, 10, 18, 22, 35, 37
728, 21, 24, 27
729, 33, 39
730, 27, 28
731, 6, 10, 44
732, 22
733, 0, 46
734, 16, 32, 45
735, 3, 9, 37, 42, 44
736, 19, 21, 23, 27, 30
737, 5, 19, 30
738, 5, 15, 19, 22, 23
739, 5, 22
740, 3, 18, 35
741, 17, 29, 47
742, 12, 26, 31, 36, 41, 48
743, 3, 18, 35
744, 10
745, 7, 15
746, 28, 43, 49
747, 12, 27, 28
748, 1, 19
749, 17, 21
750, 0, 18, 24, 43, 48
751, 16, 32, 45
752, 0, 11, 33
753, 3
754, 9, 15, 40
755, 12, 30, 49
756, 45
757, 23, 24, 40, 41, 43
758, 14, 40, 44
759, 15, 41, 47
760, 27, 28, 29
761, 0, 2, 23, 46
762, 7, 8, 11, 20
763, 6, 15, 22, 32
764, 5, 13, 26
765, 2, 20
766, 1, 7, 15, 48
767, 34, 45
768, 12, 24, 31, 46
769, 26, 27, 28
770, 23, 24, 40, 41
771, 20, 27, 29
772, 26
773, 27, 28
774, 1, 13, 29
775, 11, 23, 25, 36, 38, 45
776, 17, 29, 47
777, 22, 30, 39
778, 33, 42, 45, 47
779, 0, 2, 12, 39, 41, 46, 49
780, 12, 31, 36, 48
781, 12, 17, 27, 43, 45
782, 17, 47
783, 12, 31, 36, 48
784, 8, 20, 29, 32, 46
785, 10, 22, 23, 26, 36
786, 7, 20, 26, 44, 47
787, 2, 18, 27, 28, 33
788, 14, 21, 23, 24, 30, 42, 46
789, 18, 35
790, 1
791, 0, 14, 20, 44, 46
792, 5, 7, 11, 24, 27
793, 0, 18, 25, 39
794, 1, 19, 27
795, 23, 24, 40, 41, 43
796, 16
797, 0, 6, 28, 33, 35, 46, 48
798, 1, 19, 44
799, 17, 29, 47
800, 6, 31
801, 23, 24, 40, 41, 43
802, 33, 42
803, 1, 3, 19, 29, 31, 44
804, 17, 29, 47
805, 27, 31, 32, 36, 46
806, 16, 32, 45
807, 1, 19, 34, 44
808, 0, 2, 7, 18, 48
809, 14, 19
810, 7, 15, 49
811, 5, 13, 22, 30
812, 17, 29, 47
813, 13, 27, 28, 42, 48
814, 1, 5, 22
815, 4, 9
816, 7, 11, 37, 45
817, 0, 3, 7, 22, 37, 39, 40
818, 1, 19
819, 22, 26
820, 33, 37, 42
821, 4, 8, 13, 27, 28, 46
822, 27, 28, 40
823, 27, 28
824, 33, 42
825, 5, 22
826, 14, 22, 44
827, 16, 32, 45
828, 3, 16, 28, 48
829, 22, 23, 24, 39
830, 15, 26, 28, 33, 36
831, 7, 15, 49
832, 15, 22, 27, 31, 33, 40
833, 18, 35, 41, 43, 49
834, 4, 9
835, 12, 31, 36
836, 1, 19, 28, 31, 38, 44, 48
837, 4, 9, 18
838, 6, 32, 34
839, 15, 42
840, 13, 27, 28, 36
841, 7, 15, 22, 37, 43, 49
842, 7, 30, 43
843, 15, 25, 49
844, 22, 33, 41
845, 34
846, 4, 14, 21, 25, 41
847, 20, 23, 33, 42
848, 9, 13, 22, 42, 45
849, 0, 14, 22, 29, 46
850, 1, 19
851, 3, 16, 32, 45
852, 4, 9
853, 4, 9, 21, 39
854, 3, 18, 39
855, 4, 13, 32
856, 17, 29, 47
857, 12, 31, 36, 48
858, 14, 15
859, 23, 46
860, 5, 22
861, 3, 18, 35
862, 12, 22, 47, 48
863, 3, 5, 18, 35
864, 23, 24, 40, 41
865, 22
866, 8, 12, 16, 18, 29, 34, 49
867, 33, 34, 42, 44
868, 13, 23, 24, 41
869, 23, 24, 40, 41, 43
870, 13, 25
871, 5, 36, 41, 42
872, 5, 22, 31, 37, 47
873, 5, 7, 20
874, 4, 14, 16, 37, 44
875, 3, 18, 35
876, 8, 21, 29, 33, 42
877, 5, 14, 18
878, 27
879, 14, 20, 22, 24
880, 1, 3, 14, 31, 44, 45, 47
881, 29, 36, 41, 46
882, 16, 32, 45
883, 23, 24, 40, 41, 43
884, 7, 11, 19, 38, 42, 43, 47
885, 0, 27, 28, 32
886, 0, 2, 28, 41, 46
887, 23, 24, 40, 41, 43
888, 3, 18, 35
889, 14, 31
890, 8, 14, 44
891, 3, 14, 18, 22, 35
892, 1, 3, 30
893, 6, 12, 41, 44
894, 11, 30, 43
895, 7, 15, 49
896, 0, 2, 46
897, 1, 17, 38, 43
898, 25, 36
899, 7, 9, 27
900, 5, 13, 22
901, 12, 31, 36, 48
902, 26, 39, 43
903, 12, 26, 38
904, 1, 16, 20, 40
905, 23, 24, 40, 41, 43
906, 6, 28, 37, 38, 49
907, 14, 16, 17, 18, 26, 31
908, 37, 44
909, 11, 30
910, 22, 28, 41, 48
911, 12, 31, 36, 48
912, 4, 5, 7, 21
913, 3, 9, 18, 35, 41
914, 5, 27, 28, 42
915, 5, 22, 31
916, 33, 42
917, 4, 9, 15
918, 7, 11, 37, 45
919, 23, 24, 40, 41, 43
920, 40
921, 1, 8, 14, 19
922, 14, 31, 44
923, 6, 28, 33, 39
924, 0, 6, 16, 30, 39, 47
925, 12, 31, 36
926, 1, 36, 46
927, 27, 42, 44
928, 4, 9
929, 20
930, 5, 22
931, 10, 16, 26
932, 13, 36, 42
933, 12, 33, 42, 47
934, 4, 27, 28
935, 1, 19, 39
936, 1, 16, 32
937, 12, 31, 36
938, 16, 32, 41, 45
939, 16, 33, 42
940, 12, 13, 31, 35, 36, 41, 44
941, 6, 9, 19, 24, 44
942, 23, 24, 40, 41, 43
943, 5, 12, 31, 36, 48
944, 0, 2, 20, 44, 46
945, 3, 18, 35
946, 4, 12, 14, 19, 32, 48
947, 41
948, 0, 14, 44
949, 1, 10, 13, 19, 25, 26, 33, 39
950, 7, 15, 16
951, 4, 29, 46
952, 14, 20, 40, 43
953, 7, 38
954, 3, 18, 45, 47
955, 19, 29, 43
956, 9, 16
957, 0, 20, 42
958, 5, 10, 32, 33, 39, 44
959, 27, 28
960, 5, 22, 25, 29, 37, 43
961, 19
962, 4, 16, 34
963, 9, 17, 44, 45
964, 7, 15, 29
965, 7, 11, 27, 37, 39, 45, 49
966, 12, 31, 36, 48
967, 34, 49
968, 31
969, 25, 33, 42, 45
970, 16, 27, 32, 45
971, 25, 41
972, 6, 9, 15, 24, 25, 40, 45
973, 7, 8, 9, 11, 29, 37, 45
974, 21, 36
975, 5, 7, 14, 17, 22
976, 38, 40
977, 2, 7, 15, 22, 25, 33, 41
978, 27, 28
979, 16, 32, 45
980, 8, 18, 28
981, 13
982, 41
983, 27, 28, 38, 48
984, 3, 18, 35
985, 16, 20, 32, 36
986, 16, 32, 45
987, 4, 9
988, 22, 31, 39
989, 0, 2, 46
990, 34
991, 0, 2, 46
992, 0
993, 3, 6, 13
994, 3, 29, 44
995, 9, 27, 28, 45
996, 2, 10, 22, 31, 33, 46
997, 2, 6, 22, 32
998, 0, 4, 9, 30, 33
999, 3, 18, 35
1000, 15, 34, 47

package second;

import java.io.BufferedReader;
import java.io.File;
import java.io.FileReader;
import java.io.IOException;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Map;
import java.util.Set;


/*
 * date:2015-06-10
 * by wenbaoli
 * 
 */
public class Apriori {

	private float min_sup;//minimum support
	private float min_conf;//minimum confidence
	
	private Map<Integer,Set<String>> TransDataBase;//transaction database
	private Integer DBnum;
	
	private Map<Integer,Map<Set<String>,Float>> freqItermSet;//frequent iterm set,from 1 to k...
	private Map<Set<String>,Set<Map<Set<String>,Float>>> associationRules;//the final associate rules


	public Apriori(Map<Integer,Set<String>> DB , float minSup, float minConf){
		this.TransDataBase = DB;
		this.min_conf = minConf;
		this.min_sup = minSup;
		this.DBnum = DB.size();
		freqItermSet =new HashMap<Integer,Map<Set<String>,Float>>();
		associationRules = new HashMap<Set<String>,Set<Map<Set<String>,Float>>>();
		
	}


	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		//initial 
		
		String file = "data/data.txt";
		String delimeter = ",";
		
		
		//load data
		Map<Integer,Set<String>> data = new HashMap<Integer,Set<String>>();
		
		int num = 0;
		try {
			File mFile = new File(file);
			FileReader fr = new FileReader(mFile);
			BufferedReader br = new BufferedReader(fr);
			String line;
			
			
			while((line=br.readLine())!= null) {
				line = line.trim();
				String[] str = line.split(delimeter);
//				int i = Integer.parseInt(str[0]);
				Set<String> set = new HashSet<String>();

				for (int i = 1; i < str.length; i++) {
					set.add(str[i].trim());
				}
				num++;
				data.put(num, set);
				
			}
			br.close();
		} catch(IOException ex) {
            ex.printStackTrace();
        } 
		Apriori ap = new Apriori(data,0.005f,0.6f);
		ap.findAllFreqItermSet();
		ap.findAssociationRules();
	}
	public void findAllFreqItermSet(){

		//找出頻繁一項集
		
		
		Map<Set<String>,Float> f1 = new HashMap<Set<String>,Float>();
		Map<Set<String>,Integer> OneItermSet = new HashMap<Set<String>,Integer>();
		Iterator<Map.Entry<Integer, Set<String>>> it = this.TransDataBase.entrySet().iterator();
		
		while(it.hasNext()){
			Map.Entry<Integer, Set<String>> entry = it.next();
			Set<String> itermSet = entry.getValue();
			for(String iterm:itermSet){
				Set<String> key = new HashSet<String>();
				key.add(iterm);
				if(!OneItermSet.containsKey(key)){
					OneItermSet.put(key, 1);
				}else{
					int value = 1 + OneItermSet.get(key);
					OneItermSet.put(key, value);
				}
			}
		}
		//找出支援度大於minSup的頻繁一項集
		Iterator<Map.Entry<Set<String>,Integer>> iter = OneItermSet.entrySet().iterator();
		while(iter.hasNext()){
			Map.Entry<Set<String>,Integer> entry = iter.next();
			//計算支援度
			Float support = new Float(entry.getValue().toString())/new Float(this.DBnum);
			if(support >= this.min_sup){
				f1.put(entry.getKey(), support);
			}
		}

		System.out.println("頻繁1" + "項集:" + f1);//列印頻繁1-項集
		System.out.println("-------------------------------------------");
		this.freqItermSet.put(1, f1);
		
		//由頻繁k項集得到頻繁k+1項集
		int k = 2;
		while(true){
			
			Set<Set<String>> candFreItermSets = this.apriori_gen(k,this.freqItermSet.get(k-1).keySet());
			Map<Set<String>,Float> freqKItermSetMap = this.getFreqKItermSet(k,candFreItermSets);
			if(!freqKItermSetMap.isEmpty()){
				this.freqItermSet.put(k, freqKItermSetMap);
			} else {
				break;
			}
			System.out.println("頻繁" + k + "項集：" + freqKItermSetMap);
			System.out.println("-------------------------------------------");
			k++;
					
		}
		
	}
	public Map<Set<String>, Float> getFreqKItermSet(int k,
			Set<Set<String>> candFreItermSets) {
		Map<Set<String>,Integer> candFreqKItermSetMap = new HashMap<Set<String>,Integer>();
		
		//掃描事物資料庫
		Iterator<Map.Entry<Integer, Set<String>>> it = this.TransDataBase.entrySet().iterator();
		//統計支援度計數
		while (it.hasNext()){
			Map.Entry<Integer, Set<String>> entry = it.next();
			Iterator<Set<String>> iter = candFreItermSets.iterator();
			while(iter.hasNext()){
				Set<String> set = iter.next();
				if(entry.getValue().containsAll(set)){
					if(!candFreqKItermSetMap.containsKey(set)){
						candFreqKItermSetMap.put(set, 1);
					}else {
						int value = 1+ candFreqKItermSetMap.get(set);
						candFreqKItermSetMap.put(set, value);
					}
				}
			}
		}
		
		Iterator<Map.Entry<Set<String>, Integer>> iter = candFreqKItermSetMap.entrySet().iterator();
		Map<Set<String>,Float> freqKIntermSet = new HashMap<Set<String>,Float>();
		while(iter.hasNext()){
			Map.Entry<Set<String>, Integer> entry = iter.next();
			float support = new Float(entry.getValue().toString())/this.DBnum;
			if(support < this.min_sup){
				iter.remove();
			} else {
				freqKIntermSet.put(entry.getKey(), support);
			}
		}
		
		return freqKIntermSet;
	}
	
	public Set<Set<String>> apriori_gen(int k, Set<Set<String>> fk){
		Set<Set<String>> ck = new HashSet<Set<String>>();
		Iterator<Set<String>> it1 = fk.iterator();
		while (it1.hasNext()) {
			Set<String> itermSet1 = it1.next();
			Iterator<Set<String>> it2 = fk.iterator();
			while (it2.hasNext()) {
				Set<String> itermSet2 = it2.next();
				if(!itermSet1.equals(itermSet2)) {
					//連線步
					Set<String> commIterms = new HashSet<String>();
					commIterms.addAll(itermSet1);
					commIterms.retainAll(itermSet2);
					if(commIterms.size() == (k - 2)){
						Set<String> candIterms = new HashSet<String>();
						candIterms.addAll(itermSet1);
						candIterms.removeAll(itermSet2);
						candIterms.addAll(itermSet2);
						//剪枝步驟
						if(!this.has_infrequent_subset(candIterms, fk)){
							ck.add(candIterms);
						}
					}
				}
			}
		}
		System.out.println(ck.size());
		return ck;
	}
	public boolean has_infrequent_subset(Set<String> set,Set<Set<String>> fk){
		Set<Set<String>> subItermSet = new HashSet<Set<String>>();
		Iterator<String> itr = set.iterator();
		while(itr.hasNext()){
			//深拷貝
			Set<String> subItem = new HashSet<String>();
			Iterator<String> it = set.iterator();
			while(it.hasNext()){
				subItem.add(it.next());
			}
			
			//去掉一個項後為k-1子集
			subItem.remove(itr.next());
			subItermSet.add(subItem);
		}
		
		Iterator<Set<String>> it = subItermSet.iterator();
		while(it.hasNext()){
			if(!fk.contains(it.next())){
				return true;
			}
		}
		return false;
	}
	public void findAssociationRulesTemp(){
		
		
	}
	public void findAssociationRules(){
		Iterator<Map.Entry<Integer, Map<Set<String>,Float>>> it = this.freqItermSet.entrySet().iterator();
		while (it.hasNext()) {
			Map.Entry<Integer, Map<Set<String>,Float>> entry = it.next();
			for (Set<String> itemSet : entry.getValue().keySet()) {
				int n = itemSet.size() / 2;
				for (int i = 1; i <= n; i++) {
					Set<Set<String>> subset = this.getProperSubset(i,itemSet);
					
					for(Set<String> conditionSet:subset){
						Set<String> conclusionSet = new HashSet<String>();
						conclusionSet.addAll(itemSet);
						conclusionSet.removeAll(conditionSet);
						int s1 = conditionSet.size();
						int s2 = conclusionSet.size();
						
						float supF = this.freqItermSet.get(s1).get(conditionSet);
						float supS = this.freqItermSet.get(s2).get(conclusionSet);
						float sup = this.freqItermSet.get(s1+s2).get(itemSet);
						
						float conf1 = sup/supF;
						float conf2 = sup/supS;
						
						if(conf1 >= this.min_conf){
							if(this.associationRules.get(conditionSet) == null){
								Set<Map<Set<String>,Float>> conclusionSetSet = new HashSet<Map<Set<String>,Float>>();
								Map<Set<String>,Float> sets = new HashMap<Set<String>,Float>();
								sets.put(conclusionSet, conf1);
								conclusionSetSet.add(sets);
								
								this.associationRules.put(conditionSet, conclusionSetSet);
								
							} else {
								Map<Set<String>,Float> sets = new HashMap<Set<String>,Float>();
								sets.put(conclusionSet, conf1);
								associationRules.get(conditionSet).add(sets);
							}
						}
						if(conf2 >= this.min_conf){
							if(this.associationRules.get(conditionSet) == null){
								Set<Map<Set<String>,Float>> conclusionSetSet = new HashSet<Map<Set<String>,Float>>();
								Map<Set<String>,Float> sets = new HashMap<Set<String>,Float>();
								sets.put(conclusionSet, conf2);
								conclusionSetSet.add(sets);
								
								this.associationRules.put(conditionSet, conclusionSetSet);
								
							} else {
								Map<Set<String>,Float> sets = new HashMap<Set<String>,Float>();
								sets.put(conclusionSet, conf2);
								associationRules.get(conditionSet).add(sets);
							}
						}
					}
				}
				
			}
			
		}
		System.out.println("關聯規則（強規則）：" + associationRules);
	}


	private Set<Set<String>> getProperSubset(int i, Set<String> itemSet) {
		
		Set<Set<String>> subset = new HashSet<Set<String>>();
		if(itemSet.size() <= 1){
			return null;
		}else if(itemSet.size() == 2){
			for(String s: itemSet){
				Set<String> set = new HashSet<String>();
				set.add(s);
				if(!subset.contains(s)){
					subset.add(set);
				}
				
			}
			return subset;
		}else {
			
			Iterator<String> it = itemSet.iterator();
			String s = it.next();
			Set<String> temp = new HashSet<String>(itemSet);
			temp.remove(s);
			//包含s的子集
			Set<Set<String>> subset0 = new HashSet<Set<String>>();
			subset0 = this.getProperSubset(i-1, temp);
			subset.addAll(subset0);
			//不包含s的子集
			Set<Set<String>> subset1 = new HashSet<Set<String>>();
			
			subset1 = this.getProperSubset(i, temp);
			subset.addAll(subset1);
			return subset;
			
			
		}
		
		
	}

}