IEEE Circuits and Systems Magazine - Q2 2020 - 40

Inference
P1 (Interictal)

argmink
P2 (Ictal)

Associative Memory (AM)

Test
Train
/Test

En

E1

C1

C64

IM

'Elec n'

LBP

6 bit
'Elec 1'

Figure 11. The architecture for Laelaps with HD computing to detect and alarm seizure [43].

Nd
S

0.5 s
En

E1

C64
LBP

Feature Extraction

6 bit

IM
C1

HD Computing: Encoding and Associative Memory

0.5 s

Training Label {1/0}

Train

< 40 s

Demux

40 	

IEEE CIRCUITS AND SYSTEMS MAGAZINE 		

4) HD Computing Using Model Compression
As a mathematical framework, HD computing can be
an alternative for machine learning problems. This
was envisioned in [50]. Due to the high dimensionality, the inference of HD computing is quite expensive,
especially when it is applied to the embedded devices with limited r- esources. For example, the memory
is limited. Therefore, reducing the high dimensionality of hypervectors without sacrificing the accuracy
has been investigated in [51]. Thus, CompHD is a
general method that compresses the model size with
the minimal loss of accuracy. The addressed hypervectors are in {-1, 1}d. Instead of Hamming distance,
the similarity metric in CompHD is cosine similarity.
To reduce the HD model size, it is natural to use
low dimensional hypervectors. However, experimental results of three practical applications using different dimensionalities in HD classification
show that the e
- fficiency is improved by reducing
model size at the cost of accuracy.
To maintain high accuracy when reducing the
dimensionality, the proposed CompHD employs
the architecture shown in Fig. 12. With no reduction in model size, C i represents the class hypervector, Q represents the query hypervector,
where 1 # i # k. In CompHD, class hypervectors
and query hypervectors are compressed, which
means the original hypervectors are divided into
s segments. To store most of the information in
original hypervectors with the full size, using
Hadamard method [52], CompHD generates P 1,
P 2, f, Ps, which are in {-1, 1}D and are orthogonal to each other, where D = d/s. Specifically, the
compressed class hypervector C l and query hypervector Ql are calculated using multiplication
and addition in HD as described by Eq. (17). By
doing so, only little information is lost when we
compress the model size, and high accuracy can
be maintained.
	

Cl =

s

/ Pi C i,

i=1

Ql =

s

/ Pi Q i (17)

i=1

Their evaluation shows that, compared to the
original HD classification that purely reduces the
dimensionality with the compression factor s = 20,
the classification accuracy for the three applications is still in an acceptable range. In particular,
maintaining the same accuracy as the original,
CompHD can on average reduce model size by
69.7% while still achieving 74% energy improvement and 4.1# execution time speedup in the context of activity recognition, gesture recognition
and valve monitoring applications [51]. Therefore,
SECOND QUARTER 2020
IEEE Circuits and Systems Magazine - Q2 2020

Table of Contents for the Digital Edition of IEEE Circuits and Systems Magazine - Q2 2020
