Hi
c1^tc2=0 is no longer true after voxel-wise conversion to z-stats.
hth
Christian
On 6 Aug 2010, at 18:42, Yiou Li wrote:
> Dear Stephen and Dr. Beckmann,
>
> I agree that the time courses are non-orthogonal, however, since their
> spatial maps are always orthogonal, the spatiotemporal component will
> always be orthogonal (as I showed before: a1*c^Tc2*a2^T), where the
> orthogonality is defined as <a1*c1^T, a2*c2^T > = 0 and <.,.> means
> inner product of two matrices.
>
> Is this right?
>
> Best,
> Leo
>
> On Thu, Aug 5, 2010 at 10:45 PM, Stephen Smith <[log in to unmask]> wrote:
>> Hi - when the ICA mixing matrix is projected back into the space of the
>> original data, to create the full timeseries associated with each ICA
>> component (i.e., when the PCA dimensionality reduction is reversed), the
>> full timecourses will not then in general be orthogonal to each other.
>> Cheers.
>>
>>
>>
>> On 5 Aug 2010, at 18:42, Yiou Li wrote:
>>
>> Hi Dr. Beckmann,
>>
>> I think there all the spatio-temporal ICs are orthogonal since FastICA
>> strictly constrains independent components to be orthogonal. That is:
>> (a1*c^Tc2*a2^T) = 0 because c1^Tc2=0, where a1 and c1 are time course
>> 1 and spatial component 1, similar definition for a2 and c2. And the
>> noise subspace is orthogonal to the ICs due to PCA.
>>
>> Where can we have non-orthogonality in this model?
>>
>> Best,
>> Leo
>>
>> On Wed, Aug 4, 2010 at 11:16 PM, Christian F. Beckmann
>> <[log in to unmask]> wrote:
>>
>> Hi
>>
>> in melodic this is a simple variance ratio test (using the spatio-temporal
>> model with and without a component). Once calcualted these % variances get
>> re-normalised (divided by their sum) due to the fact that non-orthogonality
>> means that potentially a certain bit of variance can be explained mutliple
>> times. For the 'uniquely explained' numbers the same thing is done, but
>> partialling out all other N-1 components first.
>>
>> hth
>>
>> Christian
>>
>>
>>
>> On 5 Aug 2010, at 05:36, Jack Grinband wrote:
>>
>> Hi Christian,
>>
>> So how does one calculate the % variance explained?
>>
>> thanks,
>>
>> jack
>>
>>
>>
>>
>> ---------------------------------------------------------------------------
>> Stephen M. Smith, Professor of Biomedical Engineering
>> Associate Director, Oxford University FMRIB Centre
>>
>> FMRIB, JR Hospital, Headington, Oxford OX3 9DU, UK
>> +44 (0) 1865 222726 (fax 222717)
>> [log in to unmask] http://www.fmrib.ox.ac.uk/~steve
>> ---------------------------------------------------------------------------
>>
>>
>>
>>
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