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willusually, butnotalways, resultinanQptimalsolution
path. Often, butnotalways, fewernodeswillbeexpanded
andlessarithmeticeffortrequiredthan:ifweusedA(n)
VX2+y2. Thusweseethattheformulationpresentedusesone
function, A, toembodyinaformaltheoryallknowledge
availablefromtheproblemdomain. TheselectionofA, | [
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difference favors the learning process by increasing the synaptic plasticity of certain groups of neurons. We also note an interesting point presented in [Perlovsky 2009] associating certain emotions with the need for cognition, i. e. , emotions play the role of reinforce-ment signals which drive the | [
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tion algorithm is required for comparison. Further, whilethe presented theory works for complex-valued measurement
operators, it is not straightforward to extend the current CNN
architecture to complex-valued images. Any potential solutionto this problem (e. g. , usin g the modulus, o r splitting the | [
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] |
sparse coding solver is not feed-forward, i. e. , it is an itera-
tive algorithm. On the contrary, our non-linear operator is
fully feed-forward and can be computed efficiently. If we
setf2¼1, then our non-linear operator can be considered
as a pixel-wise fully-connected layer. It is worth noting that | [
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Set5 are 32. 57 dB, which is slightly higher than the 32. 52 dB
reported in Section 4. 1. This indicates that a reasonablyFig. 4. Training with the much larger ImageNet dataset improves the
performance over the use of 91 images. Fig. 5. The figure shows the first-layer filters trained on ImageNet with an | [
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2 0. 9299 - 0. 9490 0. 9511 0. 9499 0. 9544 0. 9542
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PSNR 3 27. 54 28. 31 28. 60 28. 94 28. 65 29. 13 29. 30
4 26. 00 - 26. 81 27. 14 26. 85 27. 32 27. 50
2 0. 8687 - 0. 8993 0. 9026 0. 9004 0. 9056 0. 9067
SSIM 3 0. 7736 0. 7954 0. 8076 0. 8132 0. 8093 0. 8188 0. 8215
4 0. 7019 - 0. 7331 0. 7419 0. 7352 0. 7491 0. 7513
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] |
4 35. 71 - 37. 75 38. 26 37. 85 38. 72 38. 87
2 0. 9813 - 0. 9886 0. 9890 0. 9888 0. 9896 0. 9897
MSSSIM 3 0. 9512 0. 9595 0. 9643 0. 9653 0. 9647 0. 9669 0. 9675
4 0. 9134 - 0. 9317 0. 9338 0. 9326 0. 9371 0. 9376
TABLE 4
The Average Results of PSNR (dB), SSIM, IFC, NQM, WPSNR (dB) and MSSIM on the BSD200 Dataset | [
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SSIM 3 0. 7469 0. 7729 0. 7823 0. 7881 0. 7843 0. 7945 0. 7971
4 0. 6727 - 0. 7037 0. 7093 0. 7060 0. 7171 0. 7184
2 5. 30 - 7. 10 6. 33 7. 28 7. 51 7. 21
IFC 3 3. 05 2. 77 3. 82 3. 52 3. 91 4. 07 3. 91
4 1. 95 - 2. 45 2. 24 2. 51 2. 62 2. 45
2 36. 84 - 41. 52 38. 54 41. 72 42. 37 39. 66
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2 46. 15 - 52. 56 52. 21 52. 69 53. 56 53. 58
WPSNR 3 38. 60 40. 48 41. 39 41. 62 41. 53 42. 19 42. 29
4 34. 86 - 36. 52 36. 80 36. 64 37. 18 37. 24
2 0. 9780 - 0. 9869 0. 9876 0. 9872 0. 9883 0. 9883
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] |
quences is the following: We imagine a number of possible states G1, a2, . . . , am. For each state only certain symbols from the set 51, . . . , S«can be
transmitted (different subsets for the different states). When one of these
has been transmitted thestate changes to a new state depending both on | [
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] |
abilities p(i, j), i. e. , therelative frequency of the digram ij. The
letter frequencies p(i), (the probability ofletter i), thetransition
probabilities p;(j) and thedigram probabilities p(i, j)arerelated by
the following formulas. p(i) =Lp(i, j)=Lpel, i)
i i
p(i, . i) =p(i)p;(j)
Lp;(j) =Lp(i)=Lp(i, j)=1. | [
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0.0223738644272089,
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or of transition probabilities pi, . i", , , . •i, , _Ji n)isrequired to
specify the statistical structure. (D) Stochastic processes can also be defined which produce atext con
sisting of a sequence of "words. " Suppose there are five letters
A, B, C, D, E and 16"words" in the language with associated | [
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] |
The entropy in the case of two possibilities with probabilities Pand q=
1 - P, namely
H= - (plogP+qlogq)
isplotted in Fig. 7 as a function of p. The quantity Hhas a number ofinteresting properties which further sub
stantiate it as a reasonable measure of choice or information. /""". . . . . . . -, / \
/ \ | [
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] |
. lfATllEJIATICAL TlIEORr OFCOMMFNICATION 395
while
flex) = -LpU, j)log1:pU, j)
t. , i
H(y) Lp(i, j)log1:pCi, j). i. j i
It ISeasily shown that
tu», y)Sll(x)+H(y)
with equality only if the events areindependent (i. e. , p(i, j)=p(i)prJ»). The uncertainty of a joint event is less than orequal to the sum of the | [
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individual uncertainties. 4. Any change toward equalization of the probabilities PI, h, . . . , pn
increases H. Thus ifPI<P2and we increase PI, decreasing P2anequal
amount sothat PIand P2are more nearly equal, then Hincreases. More
generally, if we perform any "averaging" operation onthePiof the form | [
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iLldllding, P. . We first encode into a binary system. The binary code for
message sis_obtained byexpanding P, asabinary number. The expansion
is carried outtom, places, where m, is the integer satisfying:
1 1log2-<m, <1+logs -P. - p. Thus the messages of high probability arerepresented byshort codes and | [
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] |
MATHEMATICAL THEORl' OFCOMAfUNICATION 403
-~p. log r. ~H'<l~-~p. logp. AsNincreases -~p. logP. approaches H, theentropy of the source andH'
approaches H. We see from this that the inefficiency in coding, when only a finite delay of
Nsymbols is used, need not be greater than~plus the difference between | [
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] |
therate C, isthefollowing (found by a method due to R. Hamming):
Leta block of seven symbols be, 'rr, X2, •••• '(7, Ofthese X', 3, X. , X6and
)(7aremessage symbols and chosen arbitrarily bythesource. The other
three areredundant and calculated as follows:
X, Iis chosen to make a=X4+Xo+. \6+X7even
X". '2
v". q" | [
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0.0061378213576972485,
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0.044143196195364,
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] |
. 11. 4TI1EMATICAL THEORJ" OF CO. lfJll'NICATION 419
where bL, b7j, . . . b"/jare the length of the symbols which may be chosen
instate iand lead to state j. These are linear difference equations and the
behavior asL---+ ccmust be of the type
N, =AjWL
Substituting mthe difference equation. r, J1'L=L. L H'L-bj:) | [
-0.0072763171046972275,
-0.037982795387506485,
-0.020655442029237747,
0.009322557598352432,
-0.07231370359659195,
-0.0023964380379766226,
0.0006612405413761735,
0.03456326946616173,
-0.019304506480693817,
-0.031091686338186264,
0.09864702820777893,
0.012279978021979332,
0.004964869003742933,
-0.0005075419903732836,
0.005746270064264536,
-0.0759384036064148,
0.007377335336059332,
0.020209353417158127,
-0.039426762610673904,
-0.013435917906463146,
-0.026535585522651672,
-0.03131263703107834,
-0.05911970138549805,
-0.018208032473921776,
0.04147183895111084,
-0.06748643517494202,
-0.009613828733563423,
-0.058541640639305115,
-0.006585382856428623,
-0.03250298276543617,
-0.028556112200021744,
0.05773799493908882,
0.010488446801900864,
-0.007687780074775219,
0.0000020232735096215038,
-0.05594932287931442,
0.0003911420935764909,
0.04979608207941055,
-0.022129137068986893,
0.05349613353610039,
-0.10136942565441132,
-0.00816056877374649,
-0.0027609302196651697,
0.018970539793372154,
-0.00440481211990118,
-0.01935378834605217,
-0.024172881618142128,
0.0352393239736557,
-0.005236105062067509,
-0.013997457921504974,
0.017178602516651154,
-0.01409897394478321,
0.035614702850580215,
-0.014530577696859837,
0.10724680870771408,
-0.04343552887439728,
0.06216645985841751,
-0.01590452715754509,
0.017425470054149628,
0.002136782044544816,
-0.018632182851433754,
-0.07050768285989761,
-0.0025189141742885113,
-0.029553908854722977,
-0.02578127197921276,
-0.045140426605939865,
0.04566072300076485,
0.015837227925658226,
-0.010109826922416687,
0.02819589525461197,
0.09638263285160065,
-0.01660112291574478,
0.025333480909466743,
0.0672726109623909,
0.012634598650038242,
-0.028429212048649788,
0.015318114310503006,
-0.02801087684929371,
-0.030560612678527832,
-0.06876388192176819,
0.07475507259368896,
0.039143357425928116,
-0.018143313005566597,
-0.011565862223505974,
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0.06123805046081543,
0.02044808119535446,
-0.0363154411315918,
-0.046660516411066055,
-0.04818250238895416,
-0.0092144925147295,
-0.056221067905426025,
0.03037533536553383,
0.053873974829912186,
0.03682757541537285,
0.0016885321820154786,
-0.012799118645489216,
-0.028091464191675186,
-0.02400199882686138,
-0.06924429535865784,
0.04944215342402458,
0.011682144366204739,
0.019806867465376854,
0.005962449591606855,
-0.029782908037304878,
0.0651732087135315,
-0.03076300583779812,
0.020228058099746704,
0.04085120931267738,
0.09857739508152008,
-0.04678656533360481,
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] |
H=K[~Pilog~n, -~Pilognil
r'\' I 1Ii, -"i' I= - ft. . . P, 'og - = - ft. . . PiogPt'. 2";l1i
Ifthe Piare incommeasurable, they may be approximated byrationals and
the same expression must hold by our continuity assumption. Thus the
expression holds in general. The choice of coefficient Kis amatter of con | [
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] |
Information Technology, University of Technology Sydney, Ultimo, NSW2007, Australia (e-mail: zonghan. wu-3@s tudent. uts. edu. au; fengwen. chen@
student. uts. edu. au; guodong. long@ uts. edu. au; chengqi. zhang@
uts. edu. au). Shirui Pan is with the Faculty of Information Technology, Monash Univer- | [
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learning algorithms (e. g. , support vector machines for classifi-cation). Meanwhile, GNNs are deep learning models aiming at
addressing graph-related tas ks in an end-to-end manner. Many
GNNs explicitly extract high-level representations. The maindistinction between GNNs and network embedding is that | [
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] |
v+αW1σ⎛
⎝W2⎡
⎣xv,
u∈N(v)[h(t−1)
u, xu]⎤
⎦⎞
⎠
(3)where αis a hyperparameter and h(0)
vis initialized randomly. While conceptually important, SSE does not theoretically
prove that the node states will gradually converge to fixedpoints by applying (3) repeatedly. V. C
ONVOLUTIONAL GRAPH NEURAL NETWORKS | [
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] |
multiple channels. The graph convolutional layer of SpectralCNN is defined as
H
(k)
:, j=σ fk−1
i=1U(k)
i, jUTH(k−1)
:, i (j=1, 2, . . . , fk)(6)
where kis the layer index, H(k−1)∈Rn×fk−1is the input
graph signal, H(0)=X, fk−1is the number of input channels, fkis the number of output channels, and (k) | [
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same dimension as the input feature matrix Xand is not a
function of its previous hidden representation matrix H(k−1). DCNN concatenates H(1), H(2), . . . , H(K)together as the final
model outputs. As the stationary distribution of a diffusion
process is a summation of power series of probability tran- | [
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lutional layers to learn temporal and spatial dependencies, respectively. Assume that the inputs to an STGNN is a tensor
X∈R
T×n×d, and the 1-D-CNN layer slides over X[:, i, :]
along the time axis to aggregate temporal information for each
node, while the graph convolutional layer operates on X[i, :, :] | [
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(line 1. 6 is modified as follows: ; continue from 1. 0). It is argued that whenever the action’s weights converge onehas a stable control, and such a training procedure eventuallyfinds the optimal control sequence. While theory behind classical dynamic programming de-
mands choosing the optimal vector | [
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] |
method provides a good detection rate in the case of a Denial
of Service (DoS) attack and achieves a good detection rate
in the case of U2R and R2L attacks. However, the precision
of Probe, U2R and R2L is 84. 2%, 25. 0% and 89. 4%, respec-
tively. In other words, the method provided by the essay leads | [
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] |
RNN for intrusion detection, but the dataset used was the
KDD 99 Cup. Experiment accuracy, recall and precision of
Probe was 96. 6%, 97. 8% and 88. 3%, respectively; DoS was
97. 4%, 97. 05% and 99. 9%, respectively; U2R was 86. 5%, 62. 7% and 56. 1%, respectively; and R2L are 29. 73%, 28. 81%
and 94. 1%. | [
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] |
Digital Object Identifier 10. 1109/COMST. 2020. 2965856hitherto unexplored services as well as scenarios of future wireless
networks. Index Terms —Machine learning (ML), future wireless
network, deep learning, regression, classification, clustering, network association, resource allocation. NOMENCLATURE | [
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parameters. Let us assume having Nrandom train-
ing samples and Mindependent variables, formulated as
{yn, xn1, xn2, . . . , xnM}, n=1, 2, . . . , N. Then the linear
regression function can be formulated as:
yn=ε0+ε1xn1+ε2xn2+. . . +εMxnM+en, (1)
whereε0is termed as the regression intercept, while enis | [
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] |
the error term and n=1, 2, . . . , N. Hence, Eq. (1) can
be rewritten in the form of a matrix as y=Xε+e, where y=[y1, y2, . . . , yN]Tis an observation vector of
the dependent variable and e=[e1, e2, . . . , eN]T, while
ε=[ε0, ε2, . . . , ε M]TandXrepresents the observation matrix
of independent variables, given by: | [
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] |
SVM based classification can be formulated as the following
optimization problem:
max
ω, bmin
n=1, . . . , Nyn((ω
∥ω∥)T
xn+b
∥ω∥)
s. t. yn(
ωTxn+b)
≥γ, n=1, 2, . . . , N, ∥ω∥=1, (10)
w h e r ew eh a v e γ=m i n n=1, . . . , Nyn((ω
∥ω∥)Txn+b
∥ω∥). A f t e r
some further mathematical manipulations, the problem in (10) | [
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p=(yk|x1, . . . , xM)=p(yk)p(x1, . . . , xM|yk)
p(x1, . . . , xM), (13)
where p=(yk|x1, . . . , xM)is the posteriori probability, whilst p(yk)is the priori probability of yk. Given that xi
is conditionally independent of xjfori̸=j, w eh a v e :
p=(yk|x1, . . . , xM)=p(yk)
p(x1, . . . , xM)M∏
m=1p(xm|yk), (14) | [
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] |
WANG et al. : THIRTY YEARS OF ML: ROAD TO PARETO-OPTIMAL WIRELESS NETWORKS 1491
final cluster segmentation result by alternating between the
following two steps, •Step 1: In the iterative round r, assign each sample to
a cluster. For n=1, 2. . . , Nandi, k=1, 2. . . , K, i f
we have:
s(r)
i={
xn:x
n−μ(r) | [
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related. Similarly, each succeeding component tends to havethe next highest variance. These principal components can
be generated by invoking the eigenvectors of the normalized
covariance matrix. Specifically, let us consider Ntraining samples of
{x
1, x2, . . . , xN}, where xn=[xn1, xn2, . . . , xnM]Tis | [
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a reduced spatial resolution. At this stage, the size of thetemporal dimension is already relatively small (3 for gray, gradient-x, gradient-y, and 2 for optflow-x and optflow-y), so we perform convolution only in the spatial dimension at
this layer. The size of the convolution kernel used is 7/C24so | [
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has very recently emerged. This field addresses a broad rangeof problems of significant practical interest, namely, therecovery of a data matrix from what appears to be incomplete, and perhaps even corrupted, information. In its simplest form, the problem is to recover a matrix from a small sample of | [
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] |
• System identification. In control, one would like to
fit a discrete-time linear time-invariant state-spacemodel
xðtþ1Þ¼AxðtÞþBuðtÞ
yðtÞ¼CxðtÞþDuðtÞ
to a sequence of inputs uðtÞ2R
mand outputs
yðtÞ2Rp, t¼0;. . . ;N. T h ev e c t o r xðtÞ2Rnis the
state of the system at time t, a n d nis the order of | [
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] |
Even with the information that the unknown matrix M
has low rank, this problem may be severely ill posed. Here
is an example that shows why: let xbe a vector in R
nand
consider the n/C2nrank-1 matrix
M¼e1x/C3¼x1x2x3/C1/C1/C1 xn/C01xn
000 /C1/C1/C1 00
000 /C1/C1/C1 00. . . . . . . . . . . . . . . . . . | [
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reasonable random matrix models. There is, however, another condition that states the singular values of theunknown matrix cannot be too large or too small (the ratiobetween the top and lowest value must be bounded). Thisalgorithm 1) trims each row and column with too manyentries; i. e. , replaces the | [
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2.6870600110685227e-34,
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0.0019418654264882207,
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] |
F, and since
(III. 6) gives kH/C10kF/C202/C14, it suffices to bound kH/C10ckF. Note that by the Pythagorean identity, we have
kH/C10ck2
F¼P TðH/C10cÞ kk2
FþP T?ðH/C10cÞ kk2
F (III. 7)
and it is thus sufficient to bound each term in the right-
hand side. We start with the second term. Let /C3be a dual | [
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0.05113096162676811,
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0.018065499141812325,
2.441824338838146e-34,
0.004348237998783588,
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0.06286856532096863,
0.01638256385922432,
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0.05918099358677864,
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-0.0035760574974119663
] |
and let /C10be the range of P/C10)d e f i n e db y A:¼P /C10PT. T h e n
assuming that the operator A/C3A¼P TP/C10PTmapping T
onto Tis invertible (which is the case under the hypotheses
of Theorem 7), the least squares solution is given by
MOracle:¼ð A/C3AÞ/C01A/C3ðYÞ
¼Mþð A/C3AÞ/C01A/C3ðZÞ: (III. 11) | [
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] |
(III. 2) for some value of /C22, and thus one could use (IV. 1) to
solve (III. 2) by searching for the value of /C22ð/C14Þgiving
kP/C10ð^M/C0YÞkF¼/C14(assuming kP/C10ðYÞkF>/C14). We use
(IV. 1) because it works well in practice and because theFPC algorithm solves (IV. 1) nicely and accurately. We also | [
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switches to monitorthe information flow), the security of such networks is a bigconcern, especially for the applications where confidentiality hasprime importance. Therefore, in order to operate WSNs in asecure way, any kind of intrusions should be detected beforeattackers can harm the network (i. e. , | [
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sensor nodes) and/orinformation destination (i. e. , data sink or base station). In thisarticle, a survey of the state-of-the-art in Intrusion DetectionSystems (IDSs) that are proposed for WSNs is presented. Firstly, detailed information about IDSs is provided. Secondly, a briefsurvey of IDSs proposed | [
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] |
K. P. Sinaga, M. -S. Yang: U-k-means Clustering Algorithm
with splitting themselves to get better clustering. Users need
to specify a range of cluster numbers in which the true cluster
number reasonably lies and then a model selection, such as
BIC or AIC, is used to do the splitting process. Although | [
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] |
for our proposed U-k-means clustering method. In Eq. (6), ∑c
s=1αslnαsis the weighted mean of ln αkwith the weights
α1, . . . , α c. For the kth mixing proportion α(t)
k, if lnα(t)
kis
less than the weighted mean, then the new mixing propor-
tionα(t+1)
kwill become smaller than the old α(t)
k. That is, | [
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free parameters is not sufficient for the optimal solution. Instead, the single time direction networks try to make atradeoff between “remembering” the past input information, which is useful for regression (classification), and “knowledgecombining” of currently available input information. Thisresults | [
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] |
recognition rate of 65. 28% and is worse than the forwardRNN structure using one segment delay. The bidirectionalrecurrent neural network (BRNN) structure results in the best
performance (68. 53%). III. P
REDICTION ASSUMING DEPENDENT OUTPUTS
In the preceding section, we have estimated the conditional | [
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domain documents focus on different topics. Given specific domains DSandDT, when the learning
tasks TSand TTare different, then either 1) the label
spaces between the domains are different, i. e. , YS6¼Y T, o r
2) the conditional probability distributions between thedomains are different; i. e. , PðY | [
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] |
1;b2;. . . ;bsgare learned on
the source domain data by solving the optimizationproblem (2) as shown as follows:
min
a;bX
ixSi/C0X
jaj
Sibj/C13/C13/C13/C13/C13/C13/C13/C13/C13/C132
2þ/C12/C13/C13aSi/C13/C13
1
s:t: kbjk2/C201;8j21;. . . ;s :ð2Þ
In this equation, aj
Siis a new representation of basis bjfor | [
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] |
each problem can be solved by linear classifier, which is
shown as follows:
flðxÞ¼sgn/C0
wT
l/C1x/C1
;l¼1;. . . ;m :
SCL can learn a matrix W¼½w1w2. . . wm/C138of parameters. In
the third step, singular value decomposition (SVD) is applied
to matrix W¼½w1w2. . . wm/C138. Let W¼UDVT, then /C18¼UT
½1:h;:/C138 | [
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approach, the feature-representation-transfer approach, the
parameter-transfer approach, and the relational-knowledge-transfer approach, respectively. The former three contextshave an i. i. d. assumption on the data while the last context
deals with transfer learning on relational data. Most of these | [
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] |
model can share them. On the other hand, for all approaches, now different models (i. e. , different parameter sets) are fullyindependent. There are no caches for passing kernel elements
from one model to another. VI. D
ISCUSSION AND CONCLUSION
We note that a difference between all-together methods is | [
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when accessed by the CPU (host). This architecture allows
for two levels of parallelism: instruction (memory) level (i. e. , MPs) and thread level (SPs). This SIMT (Single Instruction, Multiple Threads) architecture allows for thousands or tens
of thousands of threads to be run concurrently, which is | [
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] |
bin-to-bin scores, filled with a single learnable parameter:
¯Si, N+1=¯SM+1, j=¯SM+1, N+1=z∈R. (8)
While keypoints in Awill be assigned to a single keypoint
inBor the dustbin, each dustbin has as many matches as
there are keypoints in the other set: N, Mfor dustbins
inA, Brespectively. We denote as a=[ | [
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] |
the negative log-likelihood of the assignment ¯P:
Loss =−∑
(i, j)∈Mlog¯Pi, j
−∑
i∈Ilog¯Pi, N+1−∑
j∈Jlog¯PM+1, j. (10)
This supervision aims at simultaneously maximizing the
precision and the recall of the matching. 3. 4. Comparisons to related work
The SuperGlue architecture is equivariant to permutation | [
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featuresMatcherPose estimation AUC
P MS
@5◦@10◦@20◦
ORB NN + GMS 5. 21 13. 65 25. 36 72. 0 5. 7
D2-Net NN + mutual 5. 25 14. 53 27. 96 46. 7 12. 0
ContextDesc NN + ratio test 6. 64 15. 01 25. 75 51. 2 9. 2
SIFTNN + ratio test 5. 83 13. 06 22. 47 40. 3 1. 0
NN + NG-RANSAC 6. 19 13. 80 23. 73 61. 9 0. 7 | [
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analogy that SuperGlue “glues” together local features. Local
featuresMatcherPose estimation AUC
P MS
@5◦@10◦@20◦
ContextDesc NN + ratio test 20. 16 31. 65 44. 05 56. 2 3. 3
SIFTNN + ratio test 15. 19 24. 72 35. 30 43. 4 1. 7
NN + NG-RANSAC 15. 61 25. 28 35. 87 64. 4 1. 9
NN + OANet 18. 02 28. 76 40. 31 55. 0 3. 7 | [
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2) crowding distance ( ). We now define a partial order as
if
or
and
Thatis, betweentwosolutionswithdifferingnondomination
ranks, wepreferthesolutionwiththelower(better)rank. Other-wise, if both solutions belong to the same front, then we preferthe solution that is located in a lesser crowded region. | [
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678 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE. VOL II. NO. 7. JULY IYXI). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :. . . . . . . . . . . . . . . . . . . . . . . A fd (16) Equation (16) shows that Ai, f can be computed by con- the output. All the discrete approximations A, d, f, for j < 1-2 | [
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Fig. 10. (a) Decomposition of the frequency support of the image &. if into A$, , fand the detail images D$ f. The image A‘, ‘, Jcorresponds to the lower horizontal and vertical frequencies of A, , . , _ Di, fgives the vertical high frequencies and horizontal low frequencies. G, J’the horizontal high | [
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well to the challenges associated with Big Data velocity;its incremental learning nature alleviates challenges of data
availability, real-time processing, i. i. d, and concept drift. For
example, this paradigm could be used to handle stock data
prediction due to the ever-changing and rapidly evolving | [
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age by up to a factor of 1. 5in the HSV color space. 2. 3. Inference
Just like in training, predicting detections for a test image
only requires one network evaluation. On P ASCAL VOC the
network predicts 98 bounding boxes per image and class
probabilities for each box. YOLO is extremely fast at test | [
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] |
it is classified based on the type of error:
•Correct: correct class and IOU >. 5
•Localization: correct class, . 1<IOU<. 5
•Similar: class is similar, IOU >. 1Correct: 71. 6% Correct: 65. 5%Loc: 8. 6%Sim: 4. 3%Other: 1. 9%Background: 13. 6%
Loc: 19. 0%Sim: 6. 75%Other: 4. 0%Background: 4. 75%Fast R-CNN YOLO | [
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] |
dicted by YOLO and the overlap between the two boxes. The best Fast R-CNN model achieves a mAP of 71. 8%
on the VOC 2007 test set. When combined with YOLO, its
mAP Combined Gain
Fast R-CNN 71. 8 - -
Fast R-CNN (2007 data) 66. 9 72. 4. 6
Fast R-CNN (VGG-M) 59. 2 72. 4. 6
Fast R-CNN (CaffeNet) 57. 1 72. 1. 3 | [
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] |
train-time region proposals test-time region proposals
method # boxes method # proposals mAP (%)
SS 2, 000 SS 2, 000 58. 7
EB 2, 000 EB 2, 000 58. 6
RPN+ZF, shared 2, 000 RPN+ZF, shared 300 59. 9
ablation experiments follow below
RPN+ZF, unshared 2, 000 RPN+ZF, unshared 300 58. 7
SS 2, 000 RPN+ZF 100 55. 1 | [
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SS 2, 000 RPN+ZF 300 56. 8
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SS 2, 000 RPN+ZF (no NMS) 6, 000 55. 2
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SS 2, 000 RPN+ZF (no cls) 300 51. 4
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SS 2, 000 RPN+ZF (no reg) 300 52. 1
SS 2, 000 RPN+ZF (no reg) 1, 000 51. 3
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RPN 300 07++12 70. 4 84. 9 79. 8 74. 3 53. 9 49. 8 77. 5 75. 9 88. 5 45. 6 77. 1 55. 3 86. 9 81. 7 80. 9 79. 6 40. 1 72. 6 60. 9 81. 2 61. 5
RPN 300 COCO+07++12 75:987:483:676:862:959:681:982:091:354:982:659:089:085:584:7 84:1 52:278:965. 5 85:470:2
For RPN, the train-time proposals for Fast R-CNN are 2, 000. TABLE 6 | [
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For RPN, the train-time proposals for Fast R-CNN are 2, 000. RPN* denotes the unsharing feature version. TABLE 8
Detection Results of Faster R-CNN on PASCAL VOC 2007
Test Set Using Different Settings of Anchors
settings anchor scales aspect ratios mAP (%)
1 scale, 1 ratio 1282 1:1 65. 8
2562 1:1 66. 7 | [
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] |
Assume that X∈Rm×nand the rank of X, i. e. rank(X)=r. The SVD of Xis computed as
X=U3VT(II. 9)
where U∈Rm×rwith UTU=IandV∈Rn×rwith
VTV=I. The columns of UandVare called left and
right singular vectors of X, respectively. Additionally, 3is a
diagonal matrix and its elements are composed of the singular | [
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Clearly, dltis orthogonal to Rk+1, and then
∥Rk∥2=|⟨Rt, dlt⟩|2+∥Rt+1∥2(IV. 6)
For the n-th iteration, the representation residual
∥Rn∥2≤τwhereτis a very small constant and the probe
sample ycan be formulated as:
y=n−1∑
j=1⟨Rj, dlj⟩dlj+Rn (IV. 7)
If the representation residual is small enough, the probe | [
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] |
Step 1: Compute σtexploiting Eq. V. 8 and σt←mid
(σmin, σt, σmax), where mid(·, ·, ·) denotes the
middle value of the three parameters. Step 2: While Eq. V. 9 not satisfied
doσt←γσtend
Step 3: zt+1=(zt−σt∇G(zt))+andt=t+1. End
Output: zt+1, αB. INTERIOR-POINT METHOD BASED SPARSE
REPRESENTATION STRATEGY | [
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gate gradient algorithm, and then the direction of linear search
[△α, △σ] is obtained. Second, the Lagrange dual of problem III. 12 is used to
construct the dual feasible point and duality gap:
a) The Lagrangian function and Lagrange dual of
problem III. 12 are constructed. The Lagrangian function is | [
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0.010539241135120392,
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] |
determine an optimal step size of the Newton linear search. The stopping condition of the backtracking linear search is
G(α+ηt△α, σ+ηt△σ)>G(α, σ)
+ρηt∇G(α, σ)[△α, △σ] (V. 20)
whereρ∈(0, 0. 5) andηt∈(0, 1) is the step size of the
Newton linear search. Finally, the termination condition of the Newton linear | [
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] |
and dual problems in III. 12. First, an auxiliary variable is
introduced to convert problem in III. 12 into a constrained
problem with the form of problem V. 22. Subsequently, the
alternative direction method is used to efficiently address the
sub-problems of problem V. 22. By introducing the auxiliary | [
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First, the first optimization problem V. 24(a) is considered
arg min L(s, αt, λt)=1
2τ∥s∥2+∥αt∥1−(λt)T
×(s+Xαt−y)+µ
2∥s+Xαt−y∥2
2
=1
2τ∥s∥2−(λt)Ts+µ
2∥s+Xαt−y∥2
2
+∥αt∥1−(λt)T(Xαt−y) (V. 25)
Then, it is known that the solution of problem V. 25 with
respect to sis given by
st+1=τ
1+µτ(λt−µ(y−Xαt)) (V. 26) | [
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(3) if−λ≤sj≤λ, and thenα∗
j=0. So the solution of problem VI. 6 is summarized as
α∗
j=
sj−λ, if s j>λ
sj+λ, if s j<−λ
0, otherwise(VI. 7)
The equivalent expression of the solution is
α∗=shrink (s, λ), where the j-th component of shrink (s, λ)
isshrink (s, λ)j=sign(sj) max{|sj|−λ, 0}. The operator | [
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f(α)≈1
2∥Xαt−y∥2
2+(α−αt)TXT(Xαt−y)
+1
2τ(α−αt)T(α−αt)=Qt(α, αt) (VI. 11)
Thus problem VI. 8 using the proximal algorithm can be
successively addressed by
αt+1=arg min Qt(α, αt)+λ∥α∥1 (VI. 12)
Problem VI. 12 is reformulated to a simple form of
problem VI. 6 by
Qt(α, αt)=1
2∥Xαt−y∥2
2+(α−αt)TXT(Xαt−y)
+1 | [
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imate the Hessian matrix of f(α), i. e. L(f)=2λmax(XTX). Thus, the problem VI. 8 can be converted to the problem
below:
f(α)≈1
2∥Xαt−y∥2
2+(α−αt)TXT(Xαt−y)
+L
2(α−αt)T(α−αt)=Pt(α, αt) (VI. 15)
where the solution can be reformulated as
αt+1=arg minL
2∥α−θ(αt)∥2
2+λ∥α∥1(VI. 16)
whereθ(αt)=αt−1
LXT(Xαt−y). | [
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toleranceε=10−5. Step 1:λt=max{γ∥XTyt∥∞, λ}. Step 2: Exploit shrinkage operator to solve
problem VI. 14, i. e. αi+1=shrink
(αi−τiXT(XTαt−y), λtτi). Step 3: Update the value of1
τi+1using the Eq. VI. 20. Step 4: If∥αi+1−αi∥
αi≤ε, go to step 5; Otherwise, return to step 2 and i=i+1. Step 5: yt+1=y−Xαt+1. | [
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] |
=Rλ, 1(α+τXT(y−Xα)) (VI. 26)
can be obtained which is well-defined. θ(α)=α+τXT
(y−Xα) is denoted and the resolvent operator can be
explicitly expressed as:
Rλ, 1
2(x)=(fλ, 1
2(x1), fλ, 1
2(x2), ···, fλ, 1
2(xN))T(VI. 27)
where
fλ, 1
2(xi)=2
3xi(1+cos(2π
3−2
3gλ(xi)), gλ(xi)=arg cos(λ
8(|xi|
3)−3
2) (VI. 28) | [
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] |
Input: Probe sample y, the measurement matrix X
Initialization: t=0, ε=0. 01, τ=1−ε
∥X∥2. While not converged do
Step 1: Compute θ(αt)=αt+τXT(y−Xαt). Step 2: Compute λt=√
96
9τ|[θ(αt)]k+1|3
2in Eq. VI. 31. Step 3: Apply the half proximal thresholding operator to
obtain the representation solution αt+1= | [
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] |
Specifically, the sparse representation problem III. 9 can be
viewed as an equality constrained problem and the equivalent
problem III. 12 is an unconstrained problem, which augments
the objective function of problem III. 9 with a weighted
constraint function. In this section, the augmented Lagrangian | [
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2∥y−Xα∥2
2s. t. y−Xα=0
(VI. 32)
Then, a new optimization problem VI. 32 with the form of the
Lagrangain function is reformulated as
arg min Lλ(α, z)=∥α∥1+λ
2∥y−Xα∥2
2+zT(y−Xα)
(VI. 33)
where z∈Rdis called the Lagrange multiplier vector or dual
variable and Lλ(α, z) is denoted as the augmented Lagrangian | [
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] |
Z. Zhang et al. : Survey of Sparse Representation
whereµ∈Rdis a Lagrangian multiplier and τis a penalty
parameter. Finally, the dual optimization problem VI. 43 is solved and
a similar alternating minimization idea of PALM can also be
applied to problem VI. 43, that is, zt+1=arg min
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] |
indices of all the samples in X3are all included in the
support set3. If we analyze the KKT optimality condition for
problem III. 12, we can obtain the following two equivalent
conditions of problem VII. 1, i. e. X3(y−Xα)=λu; ∥XT
3c(y−Xα)∥∞≤λ(VII. 2)
where3cdenotes the complementary set of the set 3. | [
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0.059687137603759766
] |
pi=xT
i(Xα−y), qi=xT
iXδ, ri=(1−σ)wi+σˆwi
andsi= ˆwi−wi. Thus, at the l-th stage (if ( XT
iXi)−1
exists), the update direction of the homotopy algorithm can
be computed by
δl={
(XT
3X3)−1(W−ˆW)u, on3
0, otherwise(VII. 17)
The step size which can lead to a critical point can be com-
puted byτ∗
l=min(τ+ | [
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] |
framework of dictionary learning can be generally formulated
as an optimization problem
arg min
D∈, xi{
1
NN∑
i=1(1
2∥yi−Dxi∥2
2+λP(xi))}
(VIII. 1)
where= { D=[d1, d2, ···, dM]:dT
idi=1, i=1, 2, ···, M}(Mhere may not be equal to N), Ndenotes
the number of the known data set (eg. training samples in | [
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problem VIII. 2 is converted to
arg min
X∥Y−DX∥2
Fs. t. ∥xi∥0≤k, i=1, 2, ···, N
(VIII. 3)
which is called sparse coding and kis the limit of sparsity. Then, its subproblem is considered as follows:
arg minxi∥yi−Dxi∥2
2s. t. ∥xi∥0≤k, i=1, 2, ···, N
where we can iteratively resort to the classical sparse repre- | [
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⟨D, C, X⟩=arg min
D, C, X∥(Y√µH)
−(D√µC)
X∥2
F
+η∥C∥2
Fs. t. ∥xi∥0≤k (VIII. 12)
In consideration of the KSVD algorithm, each column
of the dictionary will be normalized to l2-norm unit vector
and(DõC)
will also be normalized, and then the penalty
term∥C∥2
Fwill be dropped out and problem VIII. 12 will be | [
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] |
KSVD algorithm is applied to update Zatom by atom and
compute X. Thus Zand Xcan be obtained. Then, the
LC-KSVD algorithm normalizes dictionary D, transform
matrix A, and the classifier parameter Cby
D′=[d′
1, d′
2, ···, d′
M]=[d1
∥d1∥, d2
∥d2∥, ···, dM
∥dM∥]
A′=[a′
1, a′
2, ···, a′
M]=[a1
∥d1∥, a2
∥d2∥, ···, aM | [
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0.02281201258301735,
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0.05344989895820618,
0.023707451298832893,
0.03917725384235382,
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0.0030327371787279844,
-0.024920128285884857,
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] |
Z. Zhang et al. : Survey of Sparse Representation
function for learning a structured discriminative dictionary, which is used for pattern classification. The general model of
FDDL is formulated as
J(D, X)=arg min
D, X{f(Y, D, X)+µ∥X∥1+ηg(X)}
(VIII. 22)
where Yis the matrix composed of input data, Dis the | [
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] |
Z. Zhang et al. : Survey of Sparse Representation
be sparsely represented over a dictionary D, i. e. the solution
of the following problem is sufficiently sparse:
argminα∥α∥0s. t. Dα=z (VIII. 34)
And an equivalent problem can be reformulated for a proper
value ofλ, i. e. argminα∥Dα−z∥2
2+λ∥α∥0 (VIII. 35) | [
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practice, we do this by saving the features learned (e. g. , atregular intervals during training, to perform early stop-ping) and training a cheap classifier on top (such as a linearclassifier). However, training the final classifier can be asubstantial computational overhead (e. g. , supervised fine | [
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