Lab Seminar Chap 1 Chap 2 Chap 3

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: Multi-dimensional analysis of HRTF based on tensor singular value decomposition Daehyuk SON* System Dynamics and Applied Control Lab. (SDAC) Center for Noise and Vibration Control (No. Vi. C) KAIST 2016. 06. 17 SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 2/20 Contents § Introduction – VAD(Virtual Auditory Display) and HRTF(Head-Related Transfer Function) – Research objective § Multi-dimensional analysis of HRTF – Mean subtraction – Multi-dimensional analysis § Summary and future works Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 3/20 Virtual Auditory Display & Head-Related Transfer Function § Virtual Auditory Display (VAD) - Systems or technologies generating spatialized virtual sounds and conveying them to a listener. - To implement this technology, HRTF database is necessary. § Head Related Transfer Function (HRTF) Sound source - An acoustic transfer function between the sound pressure of sound source and that measured in front of listener’s ear drum. - Time domain HRTF is called as HRIR(Head. Related Impulse Response) Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 4/20 Research Objective For generating high quality VAD, individual HRTF is necessary. Measuring all subjects’ HRTFs is impossible. HRTF database was built. HRTF generalization and customization method was suggested. Previous methods usually limited in 2 D analysis such as median(sagittal) plane and horizontal plane. Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 5/20 Research Objective § Multi-dimensional analysis method is proposed to observe various characteristics of HRTF. – Frequency (or time) – Elevation – Azimuth – Subject – Etc. Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 6/20 Method § Tensor-singular value decomposition method – Basic concept of tensor-SVD – Equation of above figure : – Advantages • Dealing with high order data like HRTFs • Observing each dimension separately • Controlling parameters independently [1] L. Lathauwer et al. , “A multilinear singular value decomposition”, SIAM J. MATRIX ANAL. APPL. , 21(4), 2000 Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 7/20 Mean subtraction § Mean of whole dataset was subtracted in different ways. – Original data • Fourth order tensor : (Freq)*(Azi)*(Ele)*(Sub) = 456*25*49*45 – Case 1: Subtracting mean vector among all three axes except frequency axis. – Case 2: Subtracting mean matrix among two axes • Frequency-Azimuth : To reduce variation caused by azimuth axis • Frequency-Elevation : To reduce variation caused by elevation axis Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 8/20 Mean subtraction – case 1 § Mean subtraction – Original data : (Freq)*(Azi)*(Ele)*(Sub) = 456*25*49*45 – Case 1: Subtracting mean vector among all three axes • Mean vector = Freq*1 = 456*1 Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 9/20 Mean subtraction – case 1 § Decomposing simulation condition – Original data : (Freq)*(Dir)*(Sub) = 456*1225*45 – Decomposing level • Frequency axis : none • Direction axis : 1225 -> 10 • Subject axis : none – Decomposition accuracy • 87% Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 10/20 Mean subtraction – case 1 § Basis plot (subject-frequency) Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 11/20 Mean subtraction – case 1 § Scale factor plot (azimuth – elevation) Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Chap 1: Lab. Seminar Chap 2: Chap 3: Chap 4: 12/20 Mean subtraction – case 2, frequency-azimuth § Mean subtraction – Original data : (Freq)*(Azi)*(Ele)*(Sub) = 456*25*49*45 – Case 2: Subtracting mean matrix among two axes • Mean matrix = Freq*Azi = 456*25 – For reducing variation caused by azimuth axis Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 13/20 Mean subtraction – case 2, frequency-azimuth § Decomposing simulation condition – Original data : (Freq)*(Dir)*(Sub) = 456*1225*45 – Decomposing level • Frequency axis : none • Direction axis : 1225 -> 10 • Subject axis : none – Decomposition accuracy • 67% Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 14/20 Mean subtraction – case 2, frequency-azimuth § Basis plot (subject – frequency) Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 15/20 Mean subtraction – case 2, frequency-azimuth § Scale factor plot (azimuth – elevation) Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Chap 1: Lab. Seminar Chap 2: Chap 3: Chap 4: 16/20 Mean subtraction – case 2, frequency-elevation § Mean subtraction – Original data : (Freq)*(Azi)*(Ele)*(Sub) = 456*25*49*45 – Case 2: Subtracting mean matrix among two axes • Mean matrix = Freq*Ele = 456*49 – For reducing variation caused by elevation axis Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 17/20 Mean subtraction – case 2, frequency-elevation § Decomposing simulation condition – Original data : (Freq)*(Dir)*(Sub) = 456*1225*45 – Decomposing level • Frequency axis : none • Direction axis : 1225 -> 10 • Subject axis : none – Decomposition accuracy • 84% Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 18/20 Mean subtraction – case 2, frequency-elevation § Basis plot (subject – frequency) Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 19/20 Mean subtraction – case 2, frequency-elevation § Scale factor plot (azimuth – elevation) Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST

Lab. Seminar Chap 1: Chap 2: Chap 3: Chap 4: 20/20 Summary and Future works § Summary – Analysis after subtracting mean of HRTFs in various way. – Mean vector subtraction and mean matrix subtraction were proposed. § Future works – Mathematical approach will be accomplished. – Comparison between previous methods. Multi-dimensional analysis of HRTF SDAC No. Vi. C KAIST