# Independent component analysis P18

## Methods using Time Structure The model of independent component analysis (ICA) that we have considered so far consists of mixing independent random variables, usually linearly. In many applications, however, what is mixed is not random variables but time signals, or time series. This is in contrast to the basic ICA model in which the samples of have no particular order: We could shufﬂe them in any way we like, and this would have no effect on the validity of the model, nor on the estimation methods we have discussed. If the independent components (ICs) are time signals, the situation is quite. | Independent Component Analysis. Aapo Hyvarinen Juha Karhunen Erkki Oja Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-40540-X Hardback 0-471-22131-7 Electronic 18 Methods using Time Structure The model of independent component analysis ICA that we have considered so far consists of mixing independent random variables usually linearly. In many applications however what is mixed is not random variables but time signals or time series. This is in contrast to the basic ICA model in which the samples of x have no particular order We could shuffle them in any way we like and this would have no effect on the validity of the model nor on the estimation methods we have discussed. If the independent components ICs are time signals the situation is quite different. In fact if the ICs are time signals they may contain much more structure than simple random variables. For example the autocovariances covariances over different time lags of the ICs are then well-defined statistics. One can then use such additional statistics to improve the estimation of the model. This additional information can actually make the estimation of the model possible in cases where the basic ICA methods cannot estimate it for example if the ICs are gaussian but correlated over time. In this chapter we consider the estimation of the ICA model when the ICs are time signals Si t t 1 T where is the time index. In the previous chapters we denoted by t the sample index but here has a more precise meaning since it defines an order between the ICs. The model is then expressed by x i As i where A is assumed to be square as usual and the ICs are of course independent. In contrast the ICs need not be nongaussian. In the following we shall make some assumptions on the time structure of the ICs that allow for the estimation of the model. These assumptions are alternatives to the 341 342 METHODS USING TIME STRUCTURE assumption of nongaussianity made in other chapters of this book. First we shall assume that .

TÀI LIỆU LIÊN QUAN
9    196    0
31    942    42
1    833    74
89    230    12
80    304    25
51    240    8
95    377    38
1    378    17
78    197    15
91    156    6
TÀI LIỆU XEM NHIỀU
13    34775    1858
3    21970    227
25    20201    3869
20    17446    1494
16    17175    2656
14    15364    2660
1    13795    450
37    13723    2840
3    11949    226
23    11210    400
TỪ KHÓA LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
11    8    1    07-12-2022
1    6    1    07-12-2022
11    7    1    07-12-2022
6    33    1    07-12-2022
102    11    1    07-12-2022
141    8    1    07-12-2022
88    39    1    07-12-2022
7    8    1    07-12-2022
10    149    7    07-12-2022
2    152    1    07-12-2022
10    9    1    07-12-2022
9    142    1    07-12-2022
77    5    1    07-12-2022
186    3    1    07-12-2022
106    34    1    07-12-2022
12    9    1    07-12-2022
15    166    8    07-12-2022
73    8    1    07-12-2022
5    7    1    07-12-2022
83    6    1    07-12-2022
TÀI LIỆU HOT
3    21970    227
13    34775    1858
3    1807    76
580    3856    352
584    2132    88
62    4899    1
171    4286    642
2    2006    74
51    2803    158
53    3716    180
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.