I believe I have a problem understanding PCA:  I would like to use this technique to reduce the number of features of my problem. I originally have 10,000 features and 500 samples. However, the use of PCA will limit my number of principal components to the smallest between the number of samples (columns of my data matrix) and the number of features (rows of this matrix). 100% of variance could therefore be explained by 500 components. But 500 components is far smaller than 10,000 features... How can all the variance be explained by less than the number of samples (which has nothing to do with the number of features)?
In PCA, when the number of dimensions $d$ is greater than (or even equal to) the number of samples $N$, why is it that you will have at most $N-1$ non-zero eigenvectors? In other words, the rank of the covariance matrix amongst the $d\ge N$ dimensions is $N-1$.  Example: Your samples are vectorized images, which are of dimension $d = 640\times480 = 307\,200$, but you only have $N=10$ images.
It seems that containing lava in solid glass, stone and iron blocks may not be sufficient to prevent wool from burning, even if the lava is completely encased.         After some delay, it seems that fire will jump onto the wool above the iron.   Are solid blocks more effective than airspace, or not? If so, Does it matter whether the corner block is filled in? What are the exact rules on distance that I need, and how can I prevent flammable blocks from being eliminated by nearby lava? Bonus: Does a flowing lava block behave differently than a lava source block when it comes to fire creation? Back in Europe I have a N64 console. As I am currently living in Japan, I find myself tempted to buy some old N64 games in Japanese. However, the articles about the N64's region locking usually assume Japanese games on an American console...  My question thus is: Can you play a Japanese N64 Game on a European console? How can I connect a texture node to a material with Python? What does this cryptic Bash command mean? querying Recently account viewed Sending an HTTP request using QNetworkAccessManager Scale Insetted Characters to Plot How to combine an SSD boot drive with a HDD data drive? Can I boot memtest86+ if I'm using UEFI? Convert NSDate to NSString How do I convert, NSDate to NSString so that only the year in @"yyyy" format is output to the string? What's the difference between running a program as a daemon and forking it into background with '&'? What are the practical differences from a sysadmin point of view when deploying services on a unix based system? I am from Bangladesh, and I have an Indian tourist visa, which I received from the Indian High Commission in Bangladesh. At this moment I am in Bhutan. Now I want to enter India by air. Is it possible? And will I face any problems when I come back from Kolkata to Dhaka? 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Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite? I have been researching the meaning of positive semi-definite property of correlation or covariance matrices.   I am looking for any information on   Definition of positive semi-definiteness; Its important properties, practical implications; The consequence of having negative determinant, impact on multivariate analysis or simulation results etc. What happens when you target a "magical effect" with Dispel Magic? How to Give Credit for An Answer in the Comments I asked a question on SO and someone gave me the answer as a comment to the question. Subsequently, someone else gave the same answer as an answer.  I would like to give credit to the poster who made the comment. Is there any way to do that?   Being new to the site, my only thought would be to contact the commenter and tell him to post an answer if he/she wants credit. I have a few questions regarding Named Credentials. I need to perform a SOAP based call out to an external system from Sales Force. I used the wsdl2apex function to generate the class for the call out. When I started integrating this class into my process I got to thinking about securely storing the username and password for the call out, which led me to discover Named Credentials. Question is, can Named Credentials be used in the auto-generated apex class? If so, could you please provide an example?  Thanks in advance I try unsuccessfully to install the ECW support (mainly to use ECW file in QGIS 2.2). We attempt to follow and adapt the howto provided by .  My first supprise was the repository ubuntugis-unstable is unavailable for trusty and the repository  doesn't have libgdal-ecw-src package. Finally in desperation we add ubuntugis-unstable for the raring distribution in source.list.  And apply the following commands   chmod +x ERDAS-ECW_JPEG_2000_SDK-5.1.1.bin ./ERDAS-ECW_JPEG_2000_SDK-5.1.1.bin # Select option desktop read only sudo cp -r ERDAS-ECW_JPEG_2000_SDK-5.1.1 /usr/local/ sudo ln -s /usr/local/ERDAS-ECW_JPEG_2000_SDK-5.1.1/Desktop_Read-Only/lib/x86/release/libNCSEcw.so /usr/local/lib/libNCSEcw.so sudo ldconfig sudo apt-get install libgdal-ecw-src sudo gdal-ecw-build /usr/local/ERDAS-ECW_JPEG_2000_SDK-5.1.1/Desktop_Read-Only   The ECW format seems to be installed  gdalinfo --formats | grep -i ecw   ECW (rw+): ERDAS Compressed Wavelets (SDK 5.1)   JP2ECW (rw+v): ERDAS JPEG2000 (SDK 5.1)   But .... Gis crash when a ECW raster file is open with the following message :   QGIS died on signal 4Abandon (core dumped)   If anyone have an idea