Gesture Recognition Using Accelerometer

8/12/2019 Gesture Recognition Using Accelerometer

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Q Rk Y R k

Q : R k Y

Y = y1, y2, ...y N yi N

Q N x yi Rk

R 1, R 2, ...R N R i x R k yi

N

i=0R i = R k R i R j = i,j i = j

{R i } Y R i x R k

yi Q x

Q(x) = yi d(x, y i ) d(x, y j ) j = i

d(:, :)

d(x, y ) = || y x || = (y1 x1)2 + ( y2 x2)2 + ( y3 x3)2

x

R i R i

yi

yi = cent (R i )

R y R

x R

y = cent (R ) = arg miny R

{d(X, y )|X R }


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X

x x Rk y

(x |Q)

(x |Q ) = d(x, Q (x))

(x : Q) = || x Q (x)||

I = {1, 2, ...N }

Y

= {x1, x 2...x T } N N

N Y 0

N

x t ymi Y

m R mi


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S = {1, 2, ...N }

(a 11 , a 22 , a 33) t = 1 , 2, ....T

S t

P (S t |S 1, S 2, ...S t 1) = P (S t |S t 1)

A = {a ij }

a ij = P (S t = j |S t 1 = i), 1 i, j N

= { i | i = P (S 1 = i)}


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A i

N

j =1a ij = 1

N

i=1 i = 1

A


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A = {aij } =a11 a12 a13a21 a22 a23a31 a32 a33

=0.4 0.3 0.30.2 0.6 0.20.1 0.1 0.8

= { i } =123

=0.00.01.0

sunny sunny rainy rainy sunny cloud sunny ? O

O = {sun, sun, rain, rain, sun, clouds, sun }= {S 1 = 3 , S 2 = 3 , S 3 = 1 , S 4 = 1 , S 5 = 3 , S 6 = 2 , S 7 = 3}= {3, 3, 1, 1, 3, 2, 3}

{1, 2, 3}

3.a 33 .a 33.a 31 .a 11 .a 13 .a 32 .a 23

10 4


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S = {1, 2, ...N }

B = {b jk }

b jk = P (O t = ok |S t = j )

O t t V K

V = {o1, o2, ...o K }


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b jk rain, clouds, sun

rain, clouds, sun, fog, snow

= ( S,A,B,,V ) = ( A,B, )

S = {1, 2, ...N }

A = {a ij } a ij

B = {b jk } b jk ok

= { i } i

{o1, o2...o K }

O = O1, O 2, ...O T

O = O1, O 2, ..O T = ( A,B, ) P (O | )


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N T

O = O1, O 2, ...O T Q = q 1, q 2, ..q T

= ( A,B, ) P (O |


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O P (O | )

t (i)

O t i

t (i) = P (O1, O 2, ...O t , s t = i | )

t = 1 1(i) = i bi (O1) 1 i N

t t = 1 , ...T 1

t +1 ( j ) =N

i=1[ t (i)a ij ]b j (O t +1 ) 1 i N

N T

P (O | ) =N

i=1 T (i)

P (O | ) t = T


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t (i) t (i)

t (i) = P (O t +1 , O t +1 , ...O t , s t = i | )

T (i) = 1

t t = T 1, ... 1

t ( j ) =

N

i=1 ij b j (O t +1 t +1 ( j ) 1 j N

P (O | ) =N

i=1 i bi (O1) 1(i)

O

= ( A , B , )

t (i) i t

t (i) = P (S t = i |O. ) = t (i) t (i)

P (O | )

i j


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t t (i, j )

t (i, j ) = P (S t = i, S t +1 = j |O, ) = t (i)a ij b j (O t +1 ) t +1 ( j )

P (O | )

a ij = expected number of transitions form state i to state j

expected number of transitions f rom state i

= T 1t =1 t (i, j )

T 1t =1 t (i)

b j (ok ) = expected number of times in state j and observing symbol o kexpected number of times in state i

= t :O t = ok t ( j )

T t =1 t ( j )

i

a ij

i = 1(i)

= ( A,B, )

i

aij

b jk

= ( A , B , )


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P (O | )

P (B |A) P (A) P (B )

P (A |B )

P (B |A) = P (A |B )P (B )

P (A) N 1, 2.... N j

j O

P ( j |O)

P (O | , j ) O j

P (O | )

N O

P ( j ) P ( j |O)

P ( j |O) = P (O | j )P ( j )

N

i=1 P (O, i ) =

P (O | j )P ( j )N

i=1 P (O | i )P ( j )


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j P ( j |O) P ( j |O )


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N N Y 0


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O = {O(1)

, O(2)

...O(q)

}

q

O (q) = {O (q)1 , O(q)2 ....O

(q)T q }

a ij =Qq=1

1P (O q | )

T q 1t =1

qt (i)a ij b j (O

qt +1 )

qt +1 ( j )

Qq=1

1P (O q | )

T q 1t =1

qt (i)

qt (i)

b j (ok ) =Qq=1

1P (O q | ) t :O

qt = ok

qt (i)

qt ( j )

Qq=1

1P (O q | )

T qt =1

qt (i)

qt (i)

i 1 = 1


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O

P (O | ) =T

t =1aS t 1 ,S t S t = O t

O T

2.2 10 308

i

t t

p = loge p


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p = e p

p1 p2 :

p1 + ( log) p1 = ln (e p1 + e p2 )

p1 + ( log) p1 = p1 ln (1 + e( p2 p1 ))

pmin


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A =

0.3333 0.3333 0.3333 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.3333 0.3333 0.3333 0.0000 0.0000 0.0000 0.00000.0000 0.0000 0.3333 0.3333 0.3333 0.0000 0.0000 0.00000.0000 0.0000 0.0000 0.3333 0.3333 0.3333 0.0000 0.00000.0000 0.0000 0.0000 0.0000 0.3333 0.3333 0.3333 0.00000.0000 0.0000 0.0000 0.0000 0.0000 0.3333 0.3333 0.33330.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.5000 0.50000.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000

B = {b jk }

b jk = 1K

= 120

= 0 .05 1 j N, 1 k K

0 = 1

P (O | )

P (O | ) P (O | )

P (O j , )


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C = AeD


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Gesture Recognition Using Accelerometer

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